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Algebras, automorphisms, and extensions of quadratic fusion categories

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OASW01 - Structure of operator algebras: subfactors and fusion categories

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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