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One-generator braces and indecomposable set-theoretic solutions to the Yang–Baxter equation

Part of: Groups and algebras in quantum theory Other nonassociative rings and algebras Hopf algebras, quantum groups and related topics

Published online by Cambridge University Press:  06 May 2020

Wolfgang Rump
Wolfgang Rump*
Affiliation:
Institute for Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, D-70550Stuttgart, Germany ([email protected])
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Abstract

An unexpected relationship between indecomposable involutive set-theoretic solutions to the Yang–Baxter equation and one-generator braces has recently been discovered by Agata and Alicja Smoktunowicz. We extend these results and answer three open questions which arose in this context.

Keywords

Yang–Baxter equationindecomposable solutionbracecycle set

MSC classification

Primary: 17D99: None of the above, but in this section
Secondary: 16T25: Yang-Baxter equations 81R50: Quantum groups and related algebraic methods
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 63 , Issue 3 , August 2020 , pp. 676 - 696
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Copyright
Copyright © The Authors, 2020. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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Footnotes

Dedicated to B. V. M.

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