Journal ArticleDOI
Some algebraic structures connected with the Yang—Baxter equation
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This article is published in Functional Analysis and Its Applications.The article was published on 1983-01-01. It has received 728 citations till now. The article focuses on the topics: Yang–Baxter equation & Algebraic structure.read more
Citations
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On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)q
TL;DR: The quantum group SU(2)q is discussed in this paper by a method analogous to that used by Schwinger to develop the quantum theory of angular momentum such theory of the q-analogue of the quantum harmonic oscillator, as is required for this purpose.
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A q-analogue of U(g[(N+1)), Hecke algebra, and the Yang-Baxter equation
TL;DR: In this article, the structure and representations of the universal enveloping algebra U(g) were studied for g = g[(N+1) the structure of the algebra Ŭ(g), a q-analogue of the Universal Enveloping Algebra (U(g)).
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Quantum affine algebras and holonomic difference equations
Igor Frenkel,N. Yu. Reshetikhin +1 more
TL;DR: In this paper, the authors derived new holonomicq-difference equations for the matrix coefficients of the products of intertwining operators for quantum affine algebra representations of levelk.
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Universal R-matrix for quantized (super)algebras
Sergey Khoroshkin,V. N. Tolstoy +1 more
TL;DR: For quantum deformations of finite-dimensional contragredient Lie (super) algebras, the authors gave an explicit formula for the universal R-matrix, which generalizes the analogous formulae for quantized semisimple Lie algesbras obtained by M. Rosso, A. N. Kirillov, and N. Levendorskii.
References
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Partition function of the eight vertex lattice model
TL;DR: In this paper, the partition function of the zero-field eight-vertices model on a square M by N lattice is calculated exactly in the limit of M, N large.
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Quantum inverse problem method. I
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Yang-baxter equation and representation theory: i
TL;DR: In this article, the problem of constructing the GL(N,ℂ) solutions to the Yang-Baxter equation (factorizedS-matrices) is considered.