BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Daniel Gil Muñoz (University of Barcelona) DTSTART:20231004T110000Z DTEND:20231004T120000Z DTSTAMP:20260423T021527Z UID:SIMBa/14 DESCRIPTION:Title: T he use of skew braces in Hopf-Galois theory\nby Daniel Gil Muñoz (Uni versity of Barcelona) as part of Barcelona Mathematics Informal Seminar (S IMBa)\n\nLecture held in UPC (FME aula 005).\n\nAbstract\nThe notion of Ga lois extension can be rewritten in such a way that it depends only on the Galois group and its action on the top field of the extension. Moreover\, the group algebra corresponding to the Galois group can be endowed with a Hopf algebra structure. These facts inspire the notion of Hopf-Galois exte nsion: an extension that admits a Hopf algebra together with a linear acti on on the top field satisfying analogous conditions. Such a pair is called a Hopf-Galois structure. Consequently\, every Galois extension is Hopf-Ga lois\, but not the other way around. This is the beginning of Hopf-Galois theory\, a generalization of Galois theory that was introduced in the sixt ies of the last century and have provided a useful setting to generalize n otions and results from Galois theory. More recently\, it was found that e ach Hopf-Galois structure on a Galois extension corresponds to a skew brac e: a set endowed with two group structures satisfying a variant of the dis tributive property. The theory of skew braces was introduced in 2007 and o wes its interest to its applications on the study of the Yang-Baxter equat ion. This is how a connection between Hopf-Galois theory and skew braces w as established\, leading to a big body of research in the last years. In t his talk\, we provide an introduction to both of these topics as well as t heir link\, on which we shall view some recent results.\n LOCATION:https://researchseminars.org/talk/SIMBa/14/ END:VEVENT END:VCALENDAR