BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Benjamin Steinberg (CUNY) DTSTART:20220118T140000Z DTEND:20220118T160000Z DTSTAMP:20260423T023021Z UID:WienGAGT/8 DESCRIPTION:Title: Simplicity of Nekrashevych algebras of contracting self-similar groups\nby Benjamin Steinberg (CUNY) as part of Vienna Geometry and Analysis on Groups Seminar\n\n\nAbstract\nA self-similar group is a group $G$ acting on the Cayley graph of a finitely generated free monoid $X^*$ (i.e.\, regu lar rooted tree) by automorphisms in such a way that the self-similarity o f the tree is reflected in the group. The most common examples are generat ed by the states of a finite automaton. Many famous groups\, like Grigorch uk's 2-group of intermediate growth are of this form. Nekrashevych associa ted $C^*$-algebras and algebras with coefficients in a field to self-simil ar groups. In the case $G$ is trivial\, the algebra is the classical Leavi tt algebra\, a famous finitely presented simple algebra. Nekrashevych show ed that the algebra associated to the Grigorchuk group is not simple in ch aracteristic 2\, but Clark\, Exel\, Pardo\, Sims and Starling showed its N ekrashevych algebra is simple over all other fields. Nekrashevych then sho wed that the algebra associated to the Grigorchuk-Erschler group is not si mple over any field (the first such example). The Grigorchuk and Grigorchu k-Erschler groups are contracting self-similar groups. This important clas s of self-similar groups includes Gupta-Sidki p-groups and many iterated m onodromy groups like the Basilica group. Nekrashevych proved algebras asso ciated to contacting groups are finitely presented.\n\nIn this talk we dis cuss a recent result of the speaker and N. Szakacs (Manchester) characteri zing simplicity of Nekrashevych algebras of contracting groups. In particu lar\, we give an algorithm for deciding simplicity given an automaton gene rating the group. We apply our results to several families of contracting groups like Gupta-Sidki groups\, GGS groups and Sunic's generalizations of Grigorchuk's group associated to polynomials over finite fields.\n LOCATION:https://researchseminars.org/talk/WienGAGT/8/ END:VEVENT END:VCALENDAR