Deformation of YangianY(sl2)

DOI10.1080/00927879808826182zbMath0956.17005arXivq-alg/9511005OpenAlexW2037062367MaRDI QIDQ4390560

Valeriy N. Tolstoy, Sergey M. Khoroshkin, Alexander Stolin

Publication date: 18 March 2001

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/q-alg/9511005

zbMATH Keywords

classical Yang-Baxter equationquantum doubleuniversal \(R\)-matrixdeformed Yangian

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37)

Related Items

Unnamed Item ⋮ Jordanian deformation of the open \(s\ell(2)\) Gaudin model ⋮ Classical quasi-trigonometric r-matrices of Cremmer-Gervais type and their quantization ⋮ BASIC TWIST QUANTIZATION OF osp(1|2) AND κ-DEFORMATION OF D = 1 SUPERCONFORMAL MECHANICS ⋮ On some Lie bialgebra structures on polynomial algebras and their quantization ⋮ Jordanian deformation of the open XXX spin chain ⋮ One parameter family of Jordanian twists ⋮ Schrödinger sigma models and Jordanian twists ⋮ Multiparameter deformed and non-standard \(Y(\text{gl}_M)\) Yangian symmetry in a novel class of spin Calogero-Sutherland models ⋮ Algebraic Bethe ansatz for deformed Gaudin model

Cites Work

• A \(*\)-product on SL(2) and the corresponding nonstandard quantum- U\(({\mathfrak sl}(2))\)
• Isomorphism of two realizations of quantum affine algebra \(U_ q(\widehat{\mathfrak{gl}}(n))\)
• Gelfand-Tsetlin basis for representations of Yangians
• New rational solutions of Yang-Baxter equation and deformed Yangians
• Yangian double
• The Euler-Calogero-Moser model in an external potential---Yangian and loop algebra
• On rational solutions of Yang-Baxter equation for $\mathfrak{sl}(n)$.
• Yang-Baxter equation in long-range interacting systems
• Sklyanin determinant, Laplace operators, and characteristic identities for classical Lie algebras
• Symmetry of the Calogero model confined in the harmonic potential-Yangian and W algebra