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Main Authors:	Etingof, Pavel, Schedler, Travis, Soloviev, Alexandre
Format:	Preprint
Published:	1998
Subjects:	Quantum Algebra
Online Access:	https://arxiv.org/abs/math/9801047
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author	Etingof, Pavel Schedler, Travis Soloviev, Alexandre
author_facet	Etingof, Pavel Schedler, Travis Soloviev, Alexandre
contents	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.
format	Preprint
id	arxiv_https___arxiv_org_abs_math_9801047
institution	arXiv
publishDate	1998
record_format	arxiv
spellingShingle	Set-theoretical solutions to the quantum Yang-Baxter equation Etingof, Pavel Schedler, Travis Soloviev, Alexandre Quantum Algebra 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.
title	Set-theoretical solutions to the quantum Yang-Baxter equation
topic	Quantum Algebra
url	https://arxiv.org/abs/math/9801047

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