Fusion categories and finite-dimensional Hopf algebras. (Research group leaders: S. Montgomery and S. Natale.)

SONIA NATALE; SUSAN MONTGOMERY

Banff

Workshop; Workshop Women in Noncommutative Algebra and Representation Theory; 2016

Banff International Research Station

The program to classify finite-dimensional complex Hopf algebras has made great advances over the last two decades, especially for pointed Hopf algebras and semisimple Hopf algebras. A question receiving much attention of late is whether all semisimple Hopf algebras can be obtained from group algebras by a handful of constructions: bosonizations, extensions, Hopf duals, and twists. Sonia Natale answered this question affirmatively for semisimple Hopf algebras of low dimension. The categorical version of this program, the classification of fusion categories, is under active investigation by Sonia Natale and others. Fusion categories are of independent interest in several areas of mathematics, including conformal field theory and operator algebras. Moreover, Susan Montgomery has been a leading figure in the study of finite-dimensional Hopf algebras and their representations for 30 years. She has authored over 40 papers on the subject and wrote "Hopf algebras and their actions on rings" which is widely considered to be an influential text of the field. Her current research interests include the study of Frobenius-Schur indicators for semisimple Hopf algebras and fusion categories.