Universal R-matrix of reductive Lie algebras and quantum integrable systems from its colour representation
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Publication:4716620
DOI10.1088/0305-4470/28/14/026zbMATH Open0858.17012arXivhep-th/9401050OpenAlexW2043368193MaRDI QIDQ4716620
Author name not available (Why is that?)
Publication date: 25 March 1997
Published in: (Search for Journal in Brave)
Abstract: The aim of the paper is to build a universal R-matrix for the multiparameter deformation of any reductive Lie algebra. Such deformations, formulated in the recent past by Truini and Varadarajan, have the property of universality in a certain class and are shown by the present paper to be quasitriangular Hopf algebras. In order to build the R-matrix we exploit the twisting method for introducing new parameters as well as for making the transition to the reductive case. The physical motivation behind this construction is in the theory of integrable models: we intend to use such R-matrix for building the associated quantum R-matrix and Lax operators with spectral as well as color parameters - the color parameters being provided by the eigenvalues of the central generators of the reductive Lie algebra in a given representation. In this letter we present only the explicit form of the universal R-matrix of reductive Lie algebras and postpone its application to a forthcoming paper.
Full work available at URL: https://arxiv.org/abs/hep-th/9401050
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