BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Benjamin Steinberg (CCNY) DTSTART:20200929T150000Z DTEND:20200929T160000Z DTSTAMP:20260423T004038Z UID:OSUGGT/8 DESCRIPTION:Title: S implicity of Nekrashevych algebras of contracting self-similar groups\ nby Benjamin Steinberg (CCNY) as part of Ohio State Topology and Geometric Group Theory Seminar\n\n\nAbstract\nA self-similar group is a group $G$ a cting on the Cayley graph of a finitely generated free monoid $X^*$ (i.e.\ , regular rooted tree) by automorphisms in such a way that the self-simila riy of the tree is reflected in the group. The most common examples are ge nerated by the states of a finite automaton. Many famous groups like Grigo rchuk's 2-group of intermediate growth are of this form.\n\nNekrashevych a ssociated $C^*$-algebras and algebras with coefficients in a field to self -similar groups. In the case $G$ is trivial\, the algebra is the classical Leavitt algebra\, a famous finitely presented simple algebra. \n\nNekrash evych showed the algebra associated to the Grigorchuk 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 the n showed that the algebra associated to the Grigorchuk-Erschler group is n ot simple over any field (the first such example). \n\nThe Grigorchuk and Grigorchuk-Erschler groups are contracting self-similar groups. This impor tant class of self-similar groups includes Gupta-Sidki p-groups and many i terated monodromy groups like the Basilica group. Nekrashevych proved alge bras associated to contacting groups are finitely presented. \n\nIn this t alk we discuss a recent result of the speaker and N. Szakacs (York/Szeged) characterizing simplicity of Nekrashevych algebras of contracting groups. In particular\, we give an algorithm for deciding simplicity given an aut omaton generating the group. We apply our results to several families of c ontracting groups like Gupta-Sidki groups and Sunic's generalizations of G rigorchuk's group associated to polynomials over finite fields.\n LOCATION:https://researchseminars.org/talk/OSUGGT/8/ END:VEVENT END:VCALENDAR