BEGIN:VCALENDAR VERSION:2.0 CALSCALE:GREGORIAN PRODID:iCalendar-Ruby BEGIN:VEVENT CATEGORIES:Lectures & Presentations DESCRIPTION:Algebra seminar | Third Cohomology and Fusion Categories\, Marc h 21\n\nThe Mathematics Department Algebra Seminar features Darren Simmons (Ohio University) discussing "Third Cohomology and Fusion Categories" on Ma rch 21 from 4-5 p.m. via Zoom.\n\n \n\nAbstract: It was observed recently t hat for a fixed finite group $G$\, the set of all Drinfeld centers of $G$ t wisted by $3$-cocycles form a group: the so-called group of {\em modular e xtensions} (of the representation category of $G$)\, which is isomorphic to the third cohomology group of $G$ with coefficients in the multiplicative group of an algebraically closed field $F$ of characteristic zero. We show that for an Abelian $G$\, pointed twisted Drinfeld centers of $G$ form a su bgroup of the group of modular extensions. We identify this subgroup with a group of quadratic extensions containing $G$ as a Lagrangian subgroup: th e so-called group of {\em Lagrangian extensions of $G$}. We compute the gro up of Lagrangian extensions\, thereby providing an interpretation of the in ternal structure of the third cohomology group of an Abelian $G$ in terms o f fusion categories. This is joint work with Alexei Davydov. DTEND:20230321T210000Z DTSTAMP:20241123T041632Z DTSTART:20230321T200000Z LOCATION: SEQUENCE:0 SUMMARY:Algebra seminar | Third Cohomology and Fusion Categories\, March 21 UID:tag:localist.com\,2008:EventInstance_42702009039388 URL:https://calendar.ohio.edu/event/algebra_seminar_march_21 END:VEVENT END:VCALENDAR