Solutions of quantum Yang-Baxter equation related to $U_q (gl(2))$ algebra and associated integrable lattice models

Details Solutions of quantum Yang-Baxter equation related to $U_q (gl(2))$ algebra and associated integrable lattice models Solutions of quantum Yang-Baxter equation related to $U_q (gl(2))$ algebra and associated integrable lattice models

1993-12-27

arxiv.org/abs/hep-th/9312195v1

Physics

High Energy Physics

High Energy Physics - Theory

17 pages

Scientific paper

A coloured braid group representation (CBGR) is constructed with the help of some modified universal ${\cal R}$-matrix, associated to $U_q(gl(2))$ quantised algebra. Explicit realisation of Faddeev-Reshetikhin-Takhtajan (FRT) algebra is built up for this CBGR and new solutions of quantum Yang-Baxter equation are subsequently found through Yang-Baxterisation of FRT algebra. These solutions are interestingly related to nonadditive type quantum $R$-matrix and have a nontrivial $q\rightarrow 1$ limit. Lax operators of several concrete integrable models, which may be considered as some `coloured' extensions of lattice nonlinear Schr${\ddot {\rm o}}$dinger model and Toda chain, are finally obtained by taking different reductions of such solutions.

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