dc.creatorAcri, Emiliano Francisco
dc.creatorLutowski, R.
dc.creatorVendramin, Claudio Leandro
dc.date.accessioned2021-07-23T16:53:08Z
dc.date.accessioned2022-10-15T09:09:23Z
dc.date.available2021-07-23T16:53:08Z
dc.date.available2022-10-15T09:09:23Z
dc.date.created2021-07-23T16:53:08Z
dc.date.issued2019-09
dc.identifierAcri, Emiliano Francisco; Lutowski, R.; Vendramin, Claudio Leandro; Retractability of solutions to the Yang-Baxter equation and p-nilpotency of skew braces; World Scientific; International Journal of Algebra and Computation; 30; 1; 9-2019; 91-115
dc.identifier0218-1967
dc.identifierhttp://hdl.handle.net/11336/136766
dc.identifierCONICET Digital
dc.identifierCONICET
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/4368695
dc.description.abstractUsing Bieberbach groups, we study multipermutation involutive solutions to the Yang-Baxter equation. We use a linear representation of the structure group of an involutive solution to study the unique product property in such groups. An algorithm to find subgroups of a Bieberbach group isomorphic to the Promislow subgroup is introduced and then used in the case of structure group of involutive solutions. To extend the results related to retractability to non-involutive solutions, following the ideas of Meng, Ballester-Bolinches and Romero, we develop the theory of right p-nilpotent skew braces. The theory of left p-nilpotent skew braces is also developed and used to give a short proof of a theorem of Smoktunowicz in the context of skew braces.
dc.languageeng
dc.publisherWorld Scientific
dc.relationinfo:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/abs/10.1142/S0218196719500656
dc.relationinfo:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1142/S0218196719500656
dc.rightshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectBIEBERBACH GROUP
dc.subjectMULTIPERMUTATION SOLUTION
dc.subjectSET-THEORETIC SOLUTION
dc.subjectSKEW BRACE
dc.subjectUNIQUE PRODUCT PROPERTY
dc.subjectYANG-BAXTER EQUATION
dc.titleRetractability of solutions to the Yang-Baxter equation and p-nilpotency of skew braces
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:ar-repo/semantics/artículo
dc.typeinfo:eu-repo/semantics/publishedVersion


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