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dc.contributor.author
Smoktunowicz, Agata
dc.contributor.author
Vendramin, Claudio Leandro
dc.date.available
2019-11-11T20:02:58Z
dc.date.issued
2018-02
dc.identifier.citation
Smoktunowicz, Agata; Vendramin, Claudio Leandro; On skew braces; EMS Publishing House; Journal of Combinatorial Algebra; 2; 1; 2-2018; 47-86
dc.identifier.issn
2415-6302
dc.identifier.uri
http://hdl.handle.net/11336/88541
dc.description.abstract
Braces are generalizations of radical rings, introduced by Rump to study involutive non-degenerate set-theoretical solutions of the Yang-Baxter equation (YBE). Skew braces were also recently introduced as a tool to study not necessarily involutive solutions. Roughly speaking, skew braces provide group-theoretical and ring-theoretical methods to understand solutions of the YBE. It turns out that skew braces appear in many different contexts, such as near-rings, matched pairs of groups, triply factorized groups, bijective 1-cocycles and Hopf-Galois extensions. These connections and some of their consequences are explored in this paper. We produce several new families of solutions related in many different ways with rings, near-rings and groups. We also study the solutions of the YBE that skew braces naturally produce. We prove, for example, that the order of the canonical solution associated with a finite skew brace is even: it is two times the exponent of the additive group modulo its center.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
EMS Publishing House
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
BRACES
dc.subject
RADICAL RINGS
dc.subject
YANG-BAXTER
dc.subject
HOPF-GALOIS
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
On skew braces
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2019-10-21T18:54:04Z
dc.journal.volume
2
dc.journal.number
1
dc.journal.pagination
47-86
dc.journal.pais
Suiza
dc.journal.ciudad
Zürich
dc.description.fil
Fil: Smoktunowicz, Agata. University of Edinburgh; Reino Unido
dc.description.fil
Fil: Vendramin, Claudio Leandro. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
dc.journal.title
Journal of Combinatorial Algebra
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.ems-ph.org/journals/show_abstract.php?issn=2415-6302&vol=2&iss=1&rank=3
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.4171/JCA/2-1-3
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