Indecomposable Set-Theoretical Solutions to the Quantum Yang–Baxter Equation on a Set with a Prime Number of Elements
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چکیده
منابع مشابه
Indecomposable set-theoretical solutions to the Quantum Yang-Baxter Equation on a set with prime number of elements
In this paper we show that all indecomposable nondegenerate set-theoretical solutions to the Quantum Yang-Baxter equation on a set of prime order are affine, which allows us to give a complete and very simple classification of such solutions. This result is a natural application of the general theory of set-theoretical solutions to the quantum Yang-Baxter equation, developed in [ESS],[LYZ],[S] ...
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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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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...
متن کامل“set-theoretical” Solutions of the Quantum Yang-baxter Equation and a Class of Garside Groups
We establish a one-to-one correspondence between structure groups of non-degenerate, involutive and braided “set-theoretical” solutions of the quantum Yang-Baxter equation and Garside groups with a certain presentation. Moreover, we show that the solution is indecomposable if and only if its structure group is a ∆−pure
متن کاملFolding of set-theoretical solutions of the Yang-Baxter equation
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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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2001
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8842