Set-theoretical solutions to the quantum Yang-Baxter equation

Details Set-theoretical solutions to the quantum Yang-Baxter equation Set-theoretical solutions to the quantum Yang-Baxter equation

1998-01-11

arxiv.org/abs/math/9801047v2

Mathematics

Quantum Algebra

36 pages, amstex, figures, revised and expanded, contains q-alg/9707027 as a small subset

Scientific paper

In 1992 V.Drinfeld formulated a number of problems in quantum group theory. In particular, he suggested to consider ``set-theoretical'' solutions to the quantum Yang-Baxter equation, i.e. solutions given by a permutation R of the set $X\times X$, 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 geometric and algebraic interpretations of such solutions, introduce several constructions of them, and make first steps towards their classification.

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