Yangian double
type: Item
instance of: scholarly article
title: Yangian double
zbMATH Open document ID: 0860.17017
DOI: 10.1007/BF00714404
published in: Letters in Mathematical Physics
publication date: 1997-05-06T00:00:00Z
review text: The authors study the algebraic structure of the quantum double \(D\) of a Yangian \(Y(g)\) and conjecture a description of it in terms of generators and relation (this conjecture is proved when \(g=\text{sl}_2)\). A triangular decomposition of \(D\) is given along with a factorization of the canonical pairing of \(Y(g)\) with its Hopf dual inside \(D\). A factorization theorem for the universal \(R\)-matrix of \(D\) is deduced, and made explicit in the \(\text{sl}_2\) case with a conjectural formula for the \(R\)-matrix in the general case. The action of the \(R\)-matrix in tensor products of evaluation representations is computed.
reviewed by: Andrew N. Pressley
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 81T13
zbMATH DE Number: 878270
zbMATH Keywords: Yang-Baxter equation
zbMATH Keywords: Yangian double
zbMATH Keywords: universal enveloping algebra
zbMATH Keywords: quantum affine algebra
zbMATH Keywords: quantum double
zbMATH Keywords: \(R\)-matrix
author: Sergey Khoroshkin
author: Valeriy N. Tolstoy
MaRDI profile type: Publication
cites work: The quantum double in integrable quantum field theory
cites work: A new interpretation of Gelfand-Tsetlin bases
cites work: Q3819194
cites work: Isomorphism of two realizations of quantum affine algebra \(U_ q(\widehat{\mathfrak{gl}}(n))\)
cites work: Quantum affine algebras and holonomic difference equations
cites work: A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
cites work: Universal \(R\)-matrix for quantized (super)algebras
cites work: On Drinfeld's realization of quantum affine algebras
cites work: Yangians and Gelfand-Zetlin bases
cites work: Central extensions of quantum current groups
cites work: An analogue of P.B.W. theorem and the universal R-matrix for \(U_ h\mathfrak{sl}(N+1)\)
cites work: DYNAMICAL SYMMETRIES OF MASSIVE INTEGRABLE MODELS 1: FORM FACTOR BOOTSTRAP EQUATIONS AS A SPECIAL CASE OF DEFORMED KNIZHNIK-ZAMOLODCHIKOV EQUATIONS
full work available at URL: https://doi.org/10.1007/bf00714404
OpenAlex ID: W4248375527
description: scientific article; zbMATH DE number 878270