SUPER YANGIAN DOUBLE DY (gl(1|1)) AND ITS GAUSS DECOMPOSITION
نویسنده
چکیده
We extend Yangian double to super (or graded) case and give its Drinfeld generators realization by Gauss decomposition. Quantum algebras(in general meaning, it includes Yangians and quantum affine algebras etc.) are new algebraic structures discovered about ten years ago [1-4], they play important roles in the study of soluble statistical models and quantum fields theory. Quantum universal enveloping algebras of simple Lie algebras, which are related with some simple solutions (without spectral parameter) of Yang-Baxter equation, have been extensively and deeply studied in the past few years. Quantum affine algebras and Yangians are related respectively with trigonometric and rational solutions of Yang-Baxter equation, they have three realizatons in literatures: Chevalley generators, T-matrix and Drinfeld generators. The first realization was proposed independently by Drinfeld and Jimbo, the second realization has direct meaning in quantum inverse scattering method and it’s convenient to introduce central extension using this realization [5]. The isomorphism of T-matrix and Drinfeld generators realizations of quantum affine algebra was established through Gauss decomposition by Ding and Frenkel [17] . The Yangian can be viewed as a deformation of only half of the corresponding loop algebra , while Yangian double are deformation of the complete loop algebra. Yangian doubles (and with central extension) have been studied by Bernard, Khoroshkin and Iohara etc.[6-12]. The
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Universal R-matrix Of The Super Yangian Double DY (gl(1|1)) a Jin-fang Cai, bc Shi-kun Wang, a
Based on Drinfel ′ d realization of super Yangian Double DY (gl(1|1)), its pairing relations and universal R-matrix are given. By taking evaluation representation of universal R-matrix, another realization L ± (u) of DY (gl(1|1)) is obtained. These two realizations of DY (gl(1|1)) are related by the supersymmetric extension of Ding-Frenkel map. Yangian algebra was introduced by Drinfel ′ d[1, 2...
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