BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nora Szakacs (York) DTSTART:20201022T090000Z DTEND:20201022T100000Z DTSTAMP:20260419T060630Z UID:CRMDS/22 DESCRIPTION:Title: S implicity of Nekrashevych algebras of contracting self-similar groups\ nby Nora Szakacs (York) as part of Western Sydney University Abend Seminar s\n\n\nAbstract\nA self-similar group is a group G acting on the infinite |X|-regular rooted tree by automorphisms in such a way that the self-simil arity of the tree is reflected in the group. The most common examples are generated by the states of a finite automaton. Many famous groups like Gr igorchuk's 2-group of intermediate growth are of this form. Nekrashevych a ssociated C*-algebras and algebras with coefficients in a field to self-si milar groups. In the case G is trivial\, the algebra is the classical Leav itt algebra. Nekrashevych showed that the algebra associated to the Grigor chuk group is not simple in characteristic 2\, but Clark\, Exel\, Pardo\, Sims and Starling showed its Nekrashevych algebra is simple over all other fields. Nekrashevych then showed that the algebra associated to the Grigo rchuk-Erschler group is not simple over any field (the first such example) . The Grigorchuk and Grigorchuk-Erschler groups are contracting self-simil ar groups. This important class of self-similar groups includes Gupta-Sidk i p-groups and many iterated monodromy groups like the Basilica group. Nek rashevych proved algebras associated to contracting groups are finitely pr esented.\nIn this talk we discuss the simplicity of Nekrashevych algebras of contracting groups. In particular\, we give an algorithm which\, given an automaton generating the group\, outputs the characteristics over which the algebra is non-simple. We apply our results to several families of co ntracting groups like Sunic's generalizations of Grigorchuk's group associ ated to polynomials over finite fields. This work is joint with Benjamin Steinberg (City College of New York).\n LOCATION:https://researchseminars.org/talk/CRMDS/22/ END:VEVENT END:VCALENDAR