Set-theoretic solutions to the Yang–Baxter equation and generalized semi-braces
Abstract: This paper aims to introduce a construction technique of set-theoretic solutions of the Yang–Baxter equation, called strong semilattice of solutions. This technique, inspired by the strong semilattice of semigroups, allows one to obtain new solutions. In particular, this method turns out to be useful to provide non-bijective solutions of finite order. It is well-known that braces, skew braces and semi-braces are closely linked with solutions. Hence, we introduce a generalization of the algebraic structure of semi-braces based on this new construction technique of solutions.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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Set-theoretic solutions to the Yang–Baxter equation and generalized semi-braces ; volume:33 ; number:3 ; year:2021 ; pages:757-772 ; extent:16
Forum mathematicum ; 33, Heft 3 (2021), 757-772 (gesamt 16)
- Creator
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Catino, Francesco
Colazzo, Ilaria
Stefanelli, Paola
- DOI
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10.1515/forum-2020-0082
- URN
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urn:nbn:de:101:1-2412271637578.108006158620
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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15.08.2025, 7:30 AM CEST
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Associated
- Catino, Francesco
- Colazzo, Ilaria
- Stefanelli, Paola
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