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Double cover Lie group of the special orthogonal group
mathematics the spin group, denoted Spin(n), is a Lie group whose underlying manifold is the double cover of the special orthogonal group SO(n) = SO(n,
Spin_group
Non-tensorial representation of the spin group
or "spin", of the electron and other subatomic particles. Mathematically, spinors are elements of spaces carrying representations of the spin group or
Spinor
Concept in differential geometry
and the spin representation of its structure group Spin(n) on the space of spinors Δn. The bundle S is called the spinor bundle for a given spin structure
Spin_structure
Type of group in mathematics
special orthogonal group, the corresponding groups are: Spin group, Spin(n) → SO(n), Projective special orthogonal group, SO(n) → PSO(n). Spin is a 2-to-1 cover
Orthogonal_group
Topics referred to by the same term
Look up spin or spinning in Wiktionary, the free dictionary. Spin or spinning most often refers to: Spin (physics) or particle spin, a fundamental property
Spin
Algebra based on a vector space with a quadratic form
matrices Hypercomplex number Octonion Paravector Quaternion Spin group Spin structure Spinor Spinor bundle Also known as a geometric algebra (especially over
Clifford_algebra
Intrinsic quantum property of particles
Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms
Spin_(physics)
Twisted spin group
In spin geometry, a spinc group (or complex spin group) is a Lie group obtained by the spin group through twisting with the first unitary group. C stands
Spinc_group
Matrix representing a Euclidean rotation
universal covering group. Often the covering group, which in this case is called the spin group denoted by Spin(n), is simpler and more natural to work with
Rotation_matrix
Particular projective representations of the orthogonal or special orthogonal groups
In mathematics, the spin representations are particular projective representations of the orthogonal or special orthogonal groups in arbitrary dimension
Spin_representation
Nonabelian group of order 120
\operatorname {Spin} (3)\to \operatorname {SO} (3)\,} of the special orthogonal group by the spin group. It follows that the binary icosahedral group is a discrete
Binary_icosahedral_group
Relativistic wave equation describing massless fermions
the Weyl equation is a relativistic wave equation for describing massless spin-1/2 particles which have an inherent handedness, or chirality, called Weyl
Weyl_equation
Geometric structure
{\displaystyle \rho \colon {\mathrm {Spin} }(n)\to {\mathrm {SO} }(n)} of the special orthogonal group by the spin group. The spinor bundle S {\displaystyle {\mathbf
Spinor_bundle
Mathematical description of fermions
the action of the Lorentz group, which describes the symmetries of Minkowski spacetime. They occur in the relativistic spin-1/2 wave function solutions
Dirac_spinor
Group of unitary complex matrices with determinant of 1
symmetry groups of spinors, Spin(3), that enables a spinor presentation of rotations. The special unitary group SU(n) is a strictly real Lie group (vs. a
Special_unitary_group
Twisted spin group
spin geometry, a spinh group (or quaternionic spin group) is a Lie group obtained by the spin group through twisting with the first symplectic group.
Spinh_group
Action where a company splits off part as a separate entity
A corporate spin-off, also known as a spin-out, starburst or hive-off, is a type of corporate action where a company "splits off" a section as a separate
Corporate_spin-off
Representation of the symmetry group of spacetime in special relativity
finite-dimensional representation theory of the universal covering group (and also the spin group, a double cover) SL ( 2 , C ) {\displaystyle {\text{SL}}(2,\mathbb
Representation theory of the Lorentz group
Representation_theory_of_the_Lorentz_group
1998 studio album by Danny Wilde + The Rembrandts
Spin This is a solo album by The Rembrandts' Danny Wilde, released by Elektra Records in 1998. The album is credited to "Danny Wilde + The Rembrandts."
Spin_This
Classification in abstract algebra
algebra, not to the spin group. Let (V,q) be a real quadratic space. The spin group is defined inside the even Clifford algebra by Spin ( V , q ) = Pin
Classification of Clifford algebras
Classification_of_Clifford_algebras
Form of propaganda in public relations and politics
In public relations and politics, spin is a form of propaganda, achieved through knowingly providing a biased interpretation of an event. While traditional
Spin_(propaganda)
Group of flat spacetime symmetries
Lorentz-signature spin group Spin ( 1 , 3 ) {\displaystyle \operatorname {Spin} (1,3)} . The Poincaré algebra is the Lie algebra of the Poincaré group. It is a
Poincaré_group
Group that is also a differentiable manifold with group operations that are smooth
integer spin and half-integer spin in quantum mechanics. Other examples of simply connected Lie groups include the special unitary group SU(n), the spin group
Lie_group
1989 studio album by Yellowjackets
Performance, Group" category. It peaked in the top 10 on Billboard's Jazz Albums chart. Yellowjackets had originally hoped to record The Spin with Claus
The_Spin
Quantum state of a system
a triplet state, or spin triplet, is the quantum state of an object such as an electron, atom, or molecule, having a quantum spin S = 1. It has three
Triplet_state
Real square matrix whose columns and rows are orthogonal unit vectors
with a covering group of SO(n), the spin group, Spin(n). Likewise, O(n) has covering groups, the pin groups, Pin(n). For n > 2, Spin(n) is simply connected
Orthogonal_matrix
Diagram used to represent quantum field theory calculations
representations of matrix groups. The diagrammatic notation can thus greatly simplify calculations. Roger Penrose described spin networks in 1971. Spin networks have
Spin_network
Concept in topological group theory
covering group, a topological double cover in which the kernel of p has order two; examples include the spin groups, pin groups, and metaplectic groups. Roughly
Covering_group
Topics referred to by the same term
represent spins and rotations of quantum states and tensor operators. Higher spin alternating sign matrix Spin group Spin (physics)#Higher spins This disambiguation
Spin_matrix
Relationship between certain vector spaces
D4 and the associated Lie group Spin(8), the double cover of 8-dimensional rotation group SO(8), arising because the group has an outer automorphism of
Triality
Infinite-dimensional group in topology
{\displaystyle 3} -connected cover of a spin group. A string manifold is a manifold with a lifting of its frame bundle to a string group bundle. This means that in
String_group
Geometric symmetry operation
n ) {\displaystyle -1\in \mathrm {Spin} (n)} in the spin group. This is particularly confusing for even spin groups, as − I ∈ S O ( 2 n ) {\displaystyle
Point_reflection
Nonabelian group in algebraic group theory
group by the spin group. It follows that the binary tetrahedral group is a discrete subgroup of Spin(3) of order 24. The complex reflection group named 3(24)3
Binary_tetrahedral_group
Canadian toy and entertainment company
Spin Master Corp. (formerly known as Spin Master Toys) is a Canadian multinational toy and entertainment company headquartered in Toronto, Ontario. Spin
Spin_Master
Subgroup of the Clifford algebra associated to a quadratic space
group is a certain subgroup of the Clifford algebra associated to a quadratic space. It maps 2-to-1 to the orthogonal group, just as the spin group maps
Pin_group
Matrices important in quantum mechanics and the study of spin
projective representation (spin representation) of the rotation group SO(3) acting on non-relativistic particles with spin 1⁄2. The states of the particles
Pauli_matrices
Grand Unified Theory proposed in 1973
the spin group Spin(10). The shortened name SO(10) is conventional among physicists, and derives from the Lie algebra or less precisely the Lie group of
SO(10)
Topological group with compact topology
the circle group T and the torus groups Tn, the orthogonal group O(n), the special orthogonal group SO(n) and its covering spin group Spin(n), the compact
Compact_group
1997 single by Sneaker Pimps
"Spin Spin Sugar" is a song by English electronic band Sneaker Pimps, released in March 1997 by Clean Up as the fourth single from their debut studio
Spin_Spin_Sugar
Lie group of Lorentz transformations
fundamental group has order 2, and its universal cover, the indefinite spin group Spin(1, 3), is isomorphic to both the special linear group SL(2, C) and
Lorentz_group
\operatorname {Spin} (3)\to \operatorname {SO} (3)} of the special orthogonal group by the spin group. It follows that the binary octahedral group is a discrete
Binary_octahedral_group
Groups of point isometries in 3 dimensions
Spin(3) → SO(3) is the double cover of the rotation group by the spin group in 3 dimensions. (This is the only connected cover of SO(3), since Spin(3)
Point groups in three dimensions
Point_groups_in_three_dimensions
1969 studio album by Four Tops
Soul Spin is the eighth studio album by American soul music vocal group Four Tops, released by Motown. A review in Billboard recommends this album to retailers
Soul_Spin
American rock band
The Spin Doctors are an American alternative rock band from New York City, best known for their early 1990s hits "Two Princes" and "Little Miss Can't Be
Spin_Doctors
American music magazine
Spin (stylized in all caps as SPIN) is an American music magazine founded in 1985 by publisher Bob Guccione Jr. Later owned by Next Management Partners
Spin_(magazine)
Relativistic wave description of fermions
\operatorname {Spin} (1,3).} This stands in contrast to the Dirac spinors, which are only covariant under the action of the complexified spin group Spin C (
Majorana_equation
Phenomenological model in criminology
the criminal theory. The criminal spin indicates acute and chronic spin, as well as individual, group and community spin. A basic premise of this theory
Criminal_spin
Rotation group in 8-dimensional Euclidean space
SO(8) is the spin group Spin(8). The center of SO(8) is Z2, the diagonal matrices {±I} (as for all SO(2n) with 2n ≥ 4), while the center of Spin(8) is Z2×Z2
SO(8)
American media company, spin-off from Comcast
Media Group, Inc., doing business as Versant (/ˈvɜːrsənt/), is an American multinational mass media company. Formed on January 2, 2026, as a spin-off of
Versant
Low-rank isomorphisms in mathematics
between rotation groups and spinors. More precisely, these are low-rank isomorphisms or central isogenies among classical algebraic groups that arise from
Exceptional isomorphisms of classical groups
Exceptional_isomorphisms_of_classical_groups
Relativistic interaction in quantum physics
mechanics, the spin–orbit interaction (also called spin–orbit effect or spin–orbit coupling) is a relativistic interaction of a particle's spin with its motion
Spin–orbit_interaction
Clifford algebra in 4 dimensions
exponentiate to a representation of the spin group Spin ( 1 , 3 ) {\displaystyle {\text{Spin}}(1,3)} of the Lorentz group SO ( 1 , 3 ) {\displaystyle {\text{SO}}(1
Dirac_algebra
Symmetry of physical laws under a charge-conjugation transformation
transform according to the spin group. Building a principle fiber bundle with the spin group as the fiber results in a spin structure. All that is missing
C-symmetry
Object in geometric algebra
vector space V is the same thing as an element of the spin group Spin(V). We define this group below. Let V be a vector space equipped with a positive
Rotor_(mathematics)
This is an episode list for the American sitcom television series Spin City. The series, which premiered on ABC on September 17, 1996, stars Michael J
List_of_Spin_City_episodes
Topics referred to by the same term
Look up spin-off or spin off in Wiktionary, the free dictionary. Spin-off, Spin Off, Spin-Off, or Spinoff may refer to: Spinoff (media), a media work
Spin-off
American television series (1996–2002)
Spin City is an American sitcom television series that aired from September 17, 1996, to April 30, 2002, on ABC. Created by Gary David Goldberg and Bill
Spin_City
1966 studio album by Buffy Sainte-Marie
Little Wheel Spin and Spin is the third album by Buffy Sainte-Marie, released in 1966. It was her only album to reach the Top 100 of the Billboard 200
Little_Wheel_Spin_and_Spin
Spinning motion in theoretical physics
theoretical physics, the spin tensor is a quantity used to describe the rotational motion of particles in spacetime. The spin tensor has application in
Spin_tensor
Algebraic structure
homomorphism Spin ( 3 ) → SO ( 3 ) {\displaystyle \operatorname {Spin} (3)\to \operatorname {SO} (3)\,} of the special orthogonal group by the spin group. As
Binary_cyclic_group
Molecular orbital theory applied to transition metal complexes
low-spin, while the latter is called high-spin. A small ΔO can be overcome by the energetic gain from not pairing the electrons, leading to high-spin. When
Ligand_field_theory
Connection on a spinor bundle
In differential geometry and mathematical physics, a spin connection is a connection on a spinor bundle. It is induced, in a canonical manner, from the
Spin_connection
Group in mathematical representation theory
symplectic group itself, but a double cover of it. That double cover is the metaplectic group. This phenomenon is closely analogous to the role of the spin group
Metaplectic_group
Subspace defined by a polynomial of degree 2 over a field
is the spin group Spin(n), and there is a standard way to extend the spin representations of Spin(n) to representations of P. (There are two spin representations
Quadric_(algebraic_geometry)
Type of group in mathematics
corresponding simply connected cover is the spin group. In the split case this recovers the ordinary groups P G O + ( V , q ) {\displaystyle \mathrm {PGO}
Classical_group
these as discrete subgroups (point groups). The special orthogonal group has a 2-fold cover by the spin group Spin(n) → SO(n), and restricting this cover
Covering groups of the alternating and symmetric groups
Covering_groups_of_the_alternating_and_symmetric_groups
Concept in mathematics
+x_{2n-1}x_{2n}+x_{2n+1}^{2};} Cn: the symplectic group Sp(2n) over k; Dn: the spin group Spin(2n) associated to a quadratic form of dimension 2n over
Reductive_group
Aviation term for a corkscrew downward path
In flight dynamics, a spin is a special category of stall resulting in autorotation (uncommanded roll) about the aircraft's longitudinal axis and a shallow
Spin_(aerodynamics)
positive definite groups. Like the spin groups and pin groups, which are covers rather than quotients of the (special) orthogonal groups, the projective
Projective_orthogonal_group
Japanese rock band
Gacharic Spin is a Japanese rock band formed in Tokyo in 2009. Initially releasing music independently, they later signed with Victor Entertainment then
Gacharic_Spin
Special tangential structure
In spin geometry, a spinc structure (or complex spin structure) is a generalization of a spin structure. In mathematics, these are used to describe spinor
Spinc_structure
Class of spinors constructed using Clifford algebras
pure spinor. In terms of stratification of spinor modules by orbits of the spin group S p i n ( V , Q ) {\displaystyle Spin(V,Q)} , pure spinors correspond
Pure_spinor
Digital gaming and sports betting company
multi-brand online casino Spin. Super Group was founded with a focus on online gaming and sports betting. In January 2022, Super Group listed on the New York
Super_Group_(company)
Technique for isolating and observing short-lived free radical molecules
short-lived radicals was developed by several independent groups by 1968. The most commonly used spin traps are alpha-phenyl N-tertiary-butyl nitrone (PBN)
Spin_trapping
Pakistani politician and businessman
his group's business operations in the textile industry. Ejaz Textile Mills Limited was established in Bhai Pheru in 1990, followed by Ejaz Spinning Mills
Sheikh_Ejaz_Ahmad
Generators of the Clifford algebra for relativistic quantum mechanics
group is encoded in the spin group Spin(1, 3) (for real, uncharged spinors) and in the complexified spin group Spin(1, 3) for charged (Dirac) spinors
Gamma_matrices
American fashion holding company
would spin off its "cable holdings and other non-retail assets" into the new company Liberty Ventures, with Liberty Interactive to be renamed QVC Group. QVC
QVC_Group
Anticommutating number
anti-commuting Weyl spinors. Both the anti-commutation and the expression as spinors arises in a natural fashion for the spin group. In essence, the Grassmann
Grassmann_number
ability to create light forms in the air. Five unnamed members G-Wiz is a spin-off group based in a fraternity house down the road from the G-Mansion who spend
List_of_The_Boys_characters
Special tangential structure
In spin geometry, a spinh structure (or quaternionic spin structure) is a generalization of a spin structure. In mathematics, these are used to describe
Spinh_structure
Connected non-abelian Lie group lacking nontrivial connected normal subgroups
This group is not simply connected however: its universal (double) cover is the spin group. Cr has as its associated simply connected group the group of
Simple_Lie_group
Topological space with only one nontrivial homotopy group
complex spin group is a group extension 0 → K ( Z , 1 ) → Spin C ( n ) → Spin ( n ) → 0 {\displaystyle 0\to K(\mathbb {Z} ,1)\to \operatorname {Spin} ^{\mathbb
Eilenberg–MacLane_space
State space for internal degrees of freedom of a subatomic particle
number of the map. SU ( 2 ) ≅ Spin ( 3 ) {\displaystyle {\text{SU}}(2)\cong {\text{Spin}}(3)} : Part of the gauge group of the Standard model. Irreps
Multiplet
The discography of the Spin Doctors, an American rock band, consists of seven studio albums, three live albums, four compilation albums, and fourteensingles
Spin_Doctors_discography
Type of cyclic group in group theory
dicyclic group is a binary polyhedral group — it is one of the classes of subgroups of the Pin group Pin−(2), which is a subgroup of the Spin group Spin(3)
Dicyclic_group
2022 political science book
China. The authors contend that modern "spin dictators" pretend to be democrats (for example, allowing a select group of high-brow, but low-circulation, dissident
Spin_Dictators
A spin valve is a device, consisting of two or more conducting magnetic materials, whose electrical resistance can change between two values depending
Spin_valve
Mathematical group
Spin 0 ( 1 , 2 ) {\displaystyle \operatorname {Sp} (2,\mathbb {R} )\cong \operatorname {Spin} _{0}(1,2)} . This is because the special linear group
Symplectic_group
Wave which propagates through a magnetic material
In condensed matter physics, a spin wave is a propagating disturbance in the ordering of a magnetic material. These low-lying collective excitations occur
Spin_wave
Spin representations of the SO(3) group
part of the detailed algebraic discussion of the rotation group SO(3). The association of a spinor with a 2×2 complex traceless Hermitian matrix was formulated
Spinors_in_three_dimensions
Lie groups and their associated Lie algebras
table of some common Lie groups and their associated Lie algebras. The following are noted: the topological properties of the group (dimension; connectedness;
Table_of_Lie_groups
Chinese holding company
Material Technology (2002) and Zhuzhou CSR Times Electric (2006) were spin-off from the groups as listed companies. In 2015, as part of the reform of the whole
CRRC_Group
American superhero comic book series
former vampire Proinsias Cassidy cameoing as a bartender. Three six-issue spin-off limited series were also produced during the series' original run: Herogasm
The_Boys_(comics)
Tool for verifying the correctness of software models
SPIN is a general tool for verifying the correctness of concurrent software models in a rigorous and mostly automated fashion. It was written by Gerard
SPIN_model_checker
Chief executive officer of BBC Worldwide from 2004 until 2012
Architects (in the same year as John Prescott). He is currently Chairman of Spin Group Ltd, Jungle Creations Ltd, Seeker Music Publishing. "John Barry SMITH
John_Smith_(BBC_executive)
Theorem in quantum mechanics
The spin–statistics theorem proves that the observed relationship between the intrinsic spin of a particle (angular momentum not due to the orbital motion)
Spin–statistics_theorem
Representation theory of the symmetries of non-relativistic quantum space
mass and spin (normally explained in Wigner's classification of relativistic mechanics) in terms of the representation theory of the Galilean group, which
Representation theory of the Galilean group
Representation_theory_of_the_Galilean_group
Retrieved August 5, 2012. The 10 Best TV Spin-offs of All Time The 10 best (and worst) spinoff shows of all time, ranked Top 10 Worst TV Spin-Offs - TIME
List_of_television_spinoffs
Swiss multinational building materials manufacturer
strategy to focus on core markets. In January 2024, Holcim announced plans to spin off 100% of its North American operations and on June 23, 2025, the company
Holcim_Group
Aspect of mathematical representation theory
2, ..., n − 1. The spin representation of the twofold cover of an odd orthogonal group, the odd spin group, and the two half-spin representations of the
Fundamental_representation
SPIN GROUP
SPIN GROUP
Female/Male/Unisex
Korean
Korean name SHIN means "faith, trust." Compare with another form of Shin.
Girl/Female
Indian
Glowing skin
Boy/Male
Indian, Sanskrit
Skin of a Goat; Tiger Skin
Male
Japanese
(1-晋, 2-信, 3-紳, 4-心, 5-慎, 6-新, 7-進, 8-真) Japanese name SHIN means 1) "advancing," 2) "belief," 3) "gentleman," 4) "heart," 5) "humble," 6) "new," 7) "progressive," and 8) "true." Compare with another form of Shin.
Boy/Male
Australian, Spanish
Innocent
Boy/Male
Indian
Life Span
Biblical
rare; precious
Surname or Lastname
English
English : from Middle English spink ‘chaffinch’ (probably of imitative origin), hence a nickname bestowed on account of some fancied resemblance to the bird.
Surname or Lastname
English and Irish
English and Irish : (of Norman origin): habitational name from Épaignes in Eure, recorded in the Latin form Hispania in the 12th century. It seems to have been so called because it was established by colonists from Spain during the Roman Empire.English and Irish : habitational name from Espinay in Ille-et-Vilaine, Brittany, so called from a collective of Old French espine ‘thorn bush’.English and Irish : ethnic name for a Spaniard or, in the case of the Irish name, for someone returning from Spain (from Gaelic Spainneach ‘Spanish’); many Irish took refuge in Spain during the 17th century wars.
Girl/Female
Australian, Biblical, Kurdish
Bush
Girl/Female
Biblical
Rare, precious.
Girl/Female
Native American
Spins.
Boy/Male
British, Danish, English, Norwegian
Skin; Parchment
Girl/Female
Christian, Hindu, Indian
Dark Skin
Male
French
Old French name, possibly derived from the word pepin/pipin, PÉPIN means "seed of a fruit."
Male
Babylonian
, I trust in Sin!
Girl/Female
Muslim
Glowing skin
Girl/Female
Australian, Indian, Punjabi, Sikh
Quite and Gentle
Biblical
a bush, enmity
Boy/Male
Egyptian
Light skin.
SPIN GROUP
SPIN GROUP
Surname or Lastname
English
English : topographic name for someone who lived on a heath, from Middle English hÅth ‘heath’, Old English hÄð, a byform of hǣð (see Heath). This form was restricted in the Middle Ages to southeastern England, and the surname is still largely confined to Kent and Sussex. In some cases it may be a habitational name from the village of Hoath in Kent, which is named with this word.
Boy/Male
Hindu, Indian
God's Gift; One without Any Shape or Form
Girl/Female
Gujarati, Hindu, Indian
Bright Light
Boy/Male
Indian
Cute Like Rabbit
Girl/Female
Hindu, Indian
Blueness
Boy/Male
American, Anglo, Australian, British, English, Teutonic
Lives Near the Stag's Spring
Surname or Lastname
English
English : variant of Cooling.
Boy/Male
English American Celtic Welsh
From the big town.
Female
German
Variant spelling of German Clothilda, KLOTHILDA means "famous battle maid."Â
Girl/Female
American, French, Greek, Hindu, Indian, Latin
Affection; Soul; Sea Gull; Protection
SPIN GROUP
SPIN GROUP
SPIN GROUP
SPIN GROUP
SPIN GROUP
v. t.
To measure by the span of the hand with the fingers extended, or with the fingers encompassing the object; as, to span a space or distance; to span a cylinder.
imp. & p. p.
of Spin
v. i.
To practice spinning; to work at drawing and twisting threads; to make yarn or thread from fiber; as, the woman knows how to spin; a machine or jenny spins with great exactness.
a.
Like a spine in shape; slender.
n.
To thrust a spit through; to fix upon a spit; hence, to thrust through or impale; as, to spit a loin of veal.
v. t.
To draw out tediously; to form by a slow process, or by degrees; to extend to a great length; -- with out; as, to spin out large volumes on a subject.
n.
A sin offering; a sacrifice for sin.
v. t.
To cover with skin, or as with skin; hence, to cover superficially.
v. i.
To attend to a spit; to use a spit.
n.
The act of spinning; as, the spin of a top; a spin a bicycle.
v. t.
To strip off the skin or hide of; to flay; to peel; as, to skin an animal.
v. t.
To cause to turn round rapidly; to whirl; to twirl; as, to spin a top.
v. t.
To protract; to spend by delays; as, to spin out the day in idleness.
imp. & p. p.
of Spit
v. i.
To move swifty; as, to spin along the road in a carriage, on a bicycle, etc.
imp.
of Spin
v. t.
To draw out, and twist into threads, either by the hand or machinery; as, to spin wool, cotton, or flax; to spin goat's hair; to produce by drawing out and twisting a fibrous material.
a.
Full of spines; thorny; as, a spiny tree.