BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Vera Serganova (University of California\, Berkeley) DTSTART:20200703T183000Z DTEND:20200703T192000Z DTSTAMP:20260415T051241Z UID:T-Rep/1 DESCRIPTION:Title: Th e Jacobson-Morozov theorem for Lie superalgebras via semisimplification fu nctor for tensor categories\nby Vera Serganova (University of Californ ia\, Berkeley) as part of T-Rep: A midsummer night's session on representa tion theory and tensor categories\n\n\nAbstract\nThe celebrated Jacobson-M orozov theorem claims that every nilpotent element of a semisimple Lie alg ebra g can be embedded into an sl(2)-triple inside g. Let g be a Lie super algebra with reductive even part and x be an odd element of g with non-zer o nilpotent [x\,x]. We give necessary and sufficient condition when x can be embedded in osp(1|2) inside g. The proof follows the approach of Etingo f and Ostrik and involves semisimplification functor for tensor categories . Next\, we will show that for every odd x in g we can construct a symmetr ic monoidal functor between categories of representations of certain super algebras. We discuss some properties of these functors and applications of them to representation theory of superalgebras with reductive even part. We also discuss possible generalization of reductive envelope of an algebr aic group to the case of a supergroup. (Joint work with Inna Entova-Aizenb ud).\n LOCATION:https://researchseminars.org/talk/T-Rep/1/ END:VEVENT END:VCALENDAR