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In representation theory, a Yangian is an infinite-dimensional Hopf algebra, a type of a quantum group. Yangians first appeared in physics in the work
Yangian
applications in representation theory in particular to Capelli's identity, Yangian and quantum integrable systems. Manin matrices are particular examples
Manin_matrix
Gauge theory providing unifying formalism for integrable systems
also related to the Yang–Baxter equation and quantum groups such as the Yangian. The theory is similar to three-dimensional Chern–Simons theory which is
Four-dimensional Chern–Simons theory
Four-dimensional_Chern–Simons_theory
Topological quantum field theory
sigma models), the Yang–Baxter equation and quantum groups such as the Yangian which describe symmetries underpinning the integrability of the aforementioned
Chern–Simons_theory
Russian mathematician and physicist (1934–2017)
Faddeev–Jackiw quantization Quantum dilogarithm Quantum inverse scattering method Yangian Awards Dannie Heineman Prize (1975) Dirac Prize (1990) Max Planck Medal
Ludvig_Faddeev
Quantum consistency equation
trigonometric and elliptic. These are related to quantum groups known as the Yangian, affine quantum groups and elliptic algebras respectively. Set-theoretic
Yang–Baxter_equation
Ancient Chinese political-philosophy school
Although these early Daoist associations do not include Shang Yang, the Shang Yangian figure Sang Hongyang in the Han dynasty also quotes Laozi. Chao Cuo may
Legalism_(Chinese_philosophy)
German theoretical physicist
quantum field theory. His most influential work is the discovery of a hidden Yangian symmetry of scattering amplitudes in N=4 supersymmetric gauge theory together
Jan_Christoph_Plefka
Method used to solve integrable many-body quantum systems
led to the formulation of quantum groups, in particular the Yangian. The center of the Yangian, given by the quantum determinant, plays a prominent role
Quantum inverse scattering method
Quantum_inverse_scattering_method
Model of mesons in the massless quark limit
of symmetries, and an underlying quantum group symmetry (in this case, Yangian symmetry). This model admits topological solitons called skyrmions. Departures
Chiral_model
Statistical model in quantum mechanics of magnetic materials
symmetry algebras for the different models. For the XXX case this is the Yangian Y ( s l 2 ) {\displaystyle Y({\mathfrak {sl}}_{2})} , while in the XXZ
Quantum_Heisenberg_model
German physicist (born 1977)
26 March 2014. "Niklas Beisert - Integrability in Planar Ads/CFT and Yangian Symmetry". YouTube. March 2019. "Niklas Beisert: "Contractions of Integrability
Niklas_Beisert
Russian-Australian mathematician
Australian Academy of Science in 2019. Amongst other things, he has worked on Yangians and Lie algebras. He is currently a Professor in the School of Mathematics
Alexander_Molev
Superconformal Yang–Mills theory
the Bethe ansatz method. They also construct an action of the associated Yangian on scattering amplitudes. Nima Arkani-Hamed et al. have also researched
N = 4 supersymmetric Yang–Mills theory
N_=_4_supersymmetric_Yang–Mills_theory
Invertible linear endomorphism
mechanics and topology. Yang–Baxter equation Hopf algebra Lie bialgebra Yangian Braid theory Quantum groups Baxter, R. J. (1982). Exactly solved models
Yang–Baxter_operator
Hom_{Sp(N-1)}(V,W)} can have dimension greater than one. It turns out that the Yangian Y ( g l 2 ) {\displaystyle Y({\mathfrak {gl}}_{2})} , a Hopf algebra introduced
Restricted_representation
Italian-French mathematician
have included representation theory, Hecke algebra, Schur–Weyl duality, Yangians, and quantum affine algebras. She earned a doctorate in 1993 at the University
Michela_Varagnolo
Mathematical discipline
Quantum enveloping algebra Quantum KZ equations Littelmann path model Yangian Drinfeld, V. G. (1985), "Hopf algebras and the quantum Yang–Baxter equation"
Quantum_affine_algebra
Peacekeeping operation in West Africa
Liberia peacekeeping mission as a 'success'". DW. Retrieved 30 August 2022. Yangian, Kennedy L. "UNMIL Sets Up Human Rights Library in Bar Association Office"
United Nations Mission in Liberia
United_Nations_Mission_in_Liberia
Construction in algebra
M.; Ha, Z. N. C.; Talstra, J. C.; Bernard, D.; Pasquier, V. (1992). "Yangian symmetry of integrable quantum chains with long-range interactions and
Hopf_algebra
Russian mathematician
Congress of Mathematicians in Berlin. Dyson conjecture Macdonald polynomials Yangian Cherednik, Ivan (1995), "Double Affine Hecke Algebras and Macdonald's Conjectures"
Ivan_Cherednik
Chinese philosopher and politician (c. 400–c. 337 BC)
Shang Yangian Legalist, even if Han Fei advocates it. Hence, Creel would argue that Han Fei does not himself consider Shen Buhai a Shang Yangian Legalist
Shen_Buhai
wave science 1956 2019 Alexander Molev Pure mathematics, specialising in 'Yangians' 1961 2019 Surinder Singh Genetic modification of canola 2019 Catherine
List of fellows of the Australian Academy of Science
List_of_fellows_of_the_Australian_Academy_of_Science
Concept in mathematics
41h5202G. doi:10.1088/1751-8113/41/8/085202. S2CID 14109958. A. Molev, Yangians and their applications, in Handbook of algebra, Vol. 3, North-Holland,
Quasideterminant
particular examples, ideas that led to the discovery of quantum groups and Yangians. He pioneered the investigation of quantum integrable systems with boundaries
Evgeny_Sklyanin
Canadian-American physicist and academic
conducted a comprehensive examination of multiplicative representations of the Yangian double in collaboration with Bernard and Feodor Smirnov, and presented
André_LeClair
death". The New Dawn Liberia. August 19, 2019. Retrieved August 11, 2024. Yangian, Kennedy L. (August 27, 2019). "Liberia: Four Charged for 'Unprovoked'
2019_Liberian_by-elections
Election Battle". The New Dawn Liberia. allAfrica. Retrieved May 14, 2025. Yangian, Kennedy L. (November 2, 2020). "Liberia: Supreme Court Gives NEC Greenlight
2020_Liberian_by-elections
Mathematical identity concerning matrices
21..123N, doi:10.1007/BF00401646, S2CID 121856652 Nazarov, M. (1998), "Yangians and Capelli identities", Amer. Math. Soc. Transl., 181: 139–163, arXiv:q-alg/9601027
Capelli's_identity
YANGIAN
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YANGIAN
Surname or Lastname
English
English : habitational name from any of the many places throughout England named Bradley, from Old English brÄd ‘broad’ + lÄ“ah ‘woodland clearing’.Scottish : habitational name from Braidlie in Roxburghshire.Irish (Ulster) : adopted as an English equivalent of Gaelic Ó Brolcháin.
Surname or Lastname
English
English : topographic name for someone living by an alder tree (Middle English al(d)re), or by a group of alders (the surname is often found in the plural form in Middle English).English : from a Middle English personal name, representing a falling together of two Old English names, Ealdhere ‘ancient army’ and Æ{dh}elhere ‘noble army’.German : variant of Alter.Translation of Swedish Ahl.Translation of Finnish Leppanen.
Surname or Lastname
English
English : nickname from Middle English chitte ‘pup’, ‘cub’, ‘young (of an animal)’ (apparently related to Old English cī{dh} ‘shoot’, ‘sprout’).English : habitational name from a place named Chitty in the parish of Chislet, Kent, named from an Old English personal name Citta + ēg ‘island’, ‘dry ground in marsh’.Possibly an Americanized form of German Schütte (see Schutte).
Boy/Male
Tamil
Thangadurai | தாநà¯à®•à®¤à¯à®°à®¾à®ˆ
Golden king
Surname or Lastname
English
English : variant spelling of Bark.
Girl/Female
Indian, Punjabi, Sikh
Guru's Home of Soul; Guru's Temple
Boy/Male
Indian, Sanskrit
Family; Race
Boy/Male
Tamil
Refuge
Boy/Male
Tamil
One who spreads Joy, Joyous, Full of bliss
Girl/Female
Indian
Princess
YANGIAN
YANGIAN
YANGIAN
YANGIAN
YANGIAN