Friday, May 2nd, 2014
3:00pm - 4:00pm, in Science 2-065

Brianna Riepel

University of New Hampshire

Brauer-Picard Groups of Pointed Fusion Categories

Abstract: This talk will cover the necessary material to define a Brauer-Picard group for fusion categories, as well as, some recently discovered facts about Brauer-Picard groups. For a fusion category C, the Brauer-Picard group BrPic(C) is a group of equivalence classes of invertible C-bimodule categoires, described by Etingof, Nikshych, and Ostrik (2010). Brauer-Picard groups are used in the classification of extensions of a fusion category by a group. Thus, one would want to know how one could calculate the Brauer-Picard group of a fusion category. In particular, it would be good to know how to calculate the Brauer-Picard group of the categories of group graded vector spaces. The Brauer-Picard group has been calculated for group graded vector spaces where the group is Abelian. However, the Brauer-Picard group has not been calculated for most groups which are not Abelian. The calculation of certain Brauer-Picard groups of categories of group graded vector spaces where the group is not Abelian will be discussed.