An action of a tensor category C on an associative algebra A is a linear monoidal functor from C to the monoidal category of A–A bimodules. We consider the problem of classifying (unitary) actions of (unitary) fusion categories on inductive limits of semisimple associative algebras (called locally semisimple algebras). A theorem of Elliot classifies locally semisimple algebras by their ordered K0 groups. We extend this theorem to a K-theoretic classification of fusion category actions on locally semisimple algebras which have an inductive limit decomposition.
This is based on joint work with Quan Chen and Roberto Hernandez Palomares.
This video was part of the Southeastern Lie Theory Workshop XIII.
