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Uniconnected solutions to the Yang–Baxter equation arising from self-maps of groups

Part of: Hopf algebras, quantum groups and related topics Groupoids Groups and algebras in quantum theory

Published online by Cambridge University Press:  20 April 2021

Wolfgang Rump
Wolfgang Rump*
Affiliation:
Institute for Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, D-70550Stuttgart, Germany
*
e-mail: rump@mathematik.uni-stuttgart.de
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Abstract

Set-theoretic solutions to the Yang–Baxter equation can be classified by their universal coverings and their fundamental groupoids. Extending previous results, universal coverings of irreducible involutive solutions are classified in the degenerate case. These solutions are described in terms of a group with a distinguished self-map. The classification in the nondegenerate case is simplified and compared with the description in the degenerate case.

Keywords

BracescoveringsYang–Baxter equationstructure groupcycle set

MSC classification

Primary: 81R50: Quantum groups and related algebraic methods
Secondary: 16T25: Yang-Baxter equations 20L05: Groupoids (i.e. small categories in which all morphisms are isomorphisms)
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 1 , March 2022 , pp. 225 - 233
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Copyright
© Canadian Mathematical Society 2021

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