Involutive Yang-Baxter groups
نویسندگان
چکیده
منابع مشابه
Involutive Yang-baxter Groups
In 1992 Drinfeld posed the question of finding the set-theoretic solutions of the Yang-Baxter equation. Recently, Gateva-Ivanova and Van den Bergh and Etingof, Schedler and Soloviev have shown a group-theoretical interpretation of involutive non-degenerate solutions. Namely, there is a oneto-one correspondence between involutive non-degenerate solutions on finite sets and groups of I-type. A gr...
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The solvability of many 2d lattice statistical models is closely connected to the Quantum Yang-Baxter equation (QYBE) [1, 2]. Solutions of the QYBE are equivalent to weight functions of vertex models. Probably the most simple 2d integrable system is (lattice) gauge theory. The weights of the field configurations around a plaquette satisfy the QYBE Fig.1a. (The gauge group is assumed to be finit...
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We introduce and study a family of operators which act in the group algebra of a Weyl group W and provide a multiparameter solution to the quantum Yang-Baxter equations of the corresponding type. These operators are then used to derive new combinatorial properties of W and to obtain new proofs of known results concerning the Bruhat order of W. The paper is organized as follows. Section 2 is dev...
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We consider the modified (or twisted) Yang-Baxter equations for the SLq(N) groups and SLq(N |M) supergroups. The general solutions for these equations are presented in the case of the linear quantum (super)groups. The introduction of spectral parameters in the twisted Yang-Baxter equation and its solutions are also discussed. Permanent address: Bogoliubov Laboratory of Theoretical Physics, JINR...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2009
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-09-04927-7