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Yangian

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 of Ludvig Faddeev and his school in the late 1970s and early 1980s concerning the quantum inverse scattering method. The name Yangian was introduced by Vladimir Drinfeld in 1985 in honor of C.N. Yang.

Applications, Description & Representation theory

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Description

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Representation theory

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Yangian

Nodes39
Edges38
Triples105
Avg. degree1.95
Density0.051282
Components1

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Yangian

Top relations

related to References · 63
Yangian → Alexander Ivanovich, American Mathematical Society, An Introduction, Andrew Pressley, Baxter, Bernard, BF01077318, Bibcode, Cambridge, Cambridge University Press, Chari, Classical Lie Algebras, CS1, Degenerate, Denis, Doklady, Doklady Akademii Nauk SSSR, Drinfeld, Drummond, Ego Prilozheniya
related to Classical representation theory · 13
Yangian → Alexander Molev, Gelfand, Grigori, In, Ivan Cherednik, Later Olshansky, Lie, Maxim Nazarov, Nazarov, Olshansky, Tsetlin, Vitaly Tarasov, Yangians
related to Description · 12
Yangian → Drinfeld, Faddeev, For, Hopf, In, Lie, R-matrix, Replacing, RTT, The, The Yangian, This Hopf
related to Representation theory · 10
Yangian → Drinfeld, George Lusztig's, Hecke, Irreducible, Lie, Representations, Schur, The, Weyl, Yangians
is a · 2
Yangian → degeneration of the quantum loop algebra, infinite-dimensional Hopf algebra
related to Physics · 2
Yangian → Hubbard, The Yangian

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Important terminology

quantum algebra drinfeld theory yangians algebras affine physics lie hopf yang classical representation doi discovered representations 20 10 scattering r-matrix

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Yangianis ainfinite-dimensional Hopf algebra0.90text
Yangianis adegeneration of the quantum loop algebra0.90text
spin chainsinstance ofYangian appears as a symmetry group of one-dimensional exactly solvable models0.80text
Hubbard modelinstance ofYangian appears as a symmetry group of one-dimensional exactly solvable models0.80text
in models of one-dimensional relativistic quantum field theory.The most famous occurrence is in planar supersymmetric Yanginstance ofYangian appears as a symmetry group of one-dimensional exactly solvable models0.80text
Yangianrelated to Classical representation theoryGrigori0.60section
Yangianrelated to Classical representation theoryOlshansky0.60section
Yangianrelated to Classical representation theoryIvan Cherednik0.60section
Yangianrelated to Classical representation theoryIn0.60section
Yangianrelated to Classical representation theoryGelfand0.60section
Yangianrelated to Classical representation theoryTsetlin0.60section
Yangianrelated to Classical representation theoryYangians0.60section

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