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Algebras, automorphisms, and extensions of quadratic fusion categories

Presented by: 
Pinhas Grossman
Friday 27th January 2017 - 11:30 to 12:30
INI Seminar Room 1
To a finite index subfactor there is a associated a tensor category along with a distinguished algebra object. If the subfactor has finite depth, this tensor category is a fusion category. The Brauer-Picard group of a fusion category, introduced by Etingof-Nikshych-Ostrik, is the (finite) group of Morita autoequivalences. It contains as a subgroup the outer automorphism group of the fusion category. In this talk we will decribe the Brauer-Picard groups of some quadratic fusion categories as groups of automorphisms which move around certain algebra objects. Combining this description with an operator algebraic construction, we can classify graded extensions of the Asaeda-Haagerup fusion categories. This is joint work with Masaki Izumi and Noah Snyder.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons