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Licensed Unlicensed Requires Authentication Published by De Gruyter February 22, 2020

Classification of indecomposable involutive set-theoretic solutions to the Yang–Baxter equation

Wolfgang Rump
From the journal Forum Mathematicum

Abstract

Using the theory of cycle sets and braces, non-degenerate indecomposable involutive set-theoretic solutions to the Yang–Baxter equation are classified in terms of their universal coverings and their fundamental group. The universal coverings are characterized as braces with an adjoint orbit generating the additive group. Using this description, all coverings of non-degenerate indecomposable cycle sets are classified. The method is illustrated by examples.

MSC 2010: 08A05; 16T25; 81R50

Dedicated to B. V. M.



Communicated by Manfred Droste


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Received: 2019-10-04
Revised: 2020-01-27
Published Online: 2020-02-22
Published in Print: 2020-07-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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