Non-unitary set-theoretical solutions to the Quantum Yang-Baxter Equation
نویسندگان
چکیده
منابع مشابه
Non-unitary set-theoretical solutions to the Quantum Yang-Baxter Equation
We develop a theory of non-unitary set-theoretical solutions to the Quantum Yang-Baxter equation. Our results generalize those obtained by Etingof, Schedler and the author in [ESS]. We remark that some of our constructions are similar to constructions obtained by Lu, Yan and Zhu in [LYZ].
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In the paper [Dr], V.Drinfeld formulated a number of problems in quantum group theory. In particular, he suggested to consider “set-theoretical” solutions of the quantum Yang-Baxter equation, i.e. solutions given by a permutation R of the set X × X, where X is a fixed set. In this paper we study such solutions, which in addition satisfy the unitarity and nondegeneracy conditions. We discuss the...
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In the paper [Dr] V.Drinfeld formulated a number of problems in quantum group theory. In particular, he suggested to consider “set-theoretical” solutions of the quantum Yang-Baxter equation, i.e. solutions given by a permutation R of the set X ×X , where X is a fixed set. In this note we study such solutions, which satisfy the unitarity and the crossing symmetry conditions – natural conditions ...
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We establish a correspondence between the invariant subsets of a non-degenerate symmetric set-theoretical solution of the quantum Yang-Baxter equation and the parabolic subgroups of its structure group, equipped with its canonical Garside structure. Moreover, we introduce the notion of a foldable solution, which extends the one of a decomposable solution. AMS Subject Classification: 16T25, 20F36.
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Because of this, a solution of (1) gives rise to a linear representation of the braid group Bn on V⊗n for every n. In [D], Drinfel’d raised the question of finding set-theoretical solutions of the YangBaxter equation. Specifically, we consider a set S and an invertible map R : S×S → S×S. We think of the Yang-Baxter equation (1) as an equality of maps from S×S×S to S×S×S. As in the linear case, ...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2000
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2000.v7.n5.a4