Algebra and Combinatorics Seminar
Date: March 11, 2022
Time: 3:00PM - 4:00PM
Location: BLOC 302
Speaker: Harshit Yadav, Rice University
Title: Filtered Frobenius algebras in monoidal categories
Abstract: We develop filtered-graded techniques for algebras in monoidal categories with the goal of establishing a categorical version of Bongale's 1967 result: A filtered deformation of a Frobenius algebra over a field is Frobenius as well. Towards the goal, we construct a monoidal associated graded functor, building on prior works of Ardizzoni-Menini, of Galatius et al., and of Gwillian-Pavlov. We then produce equivalent conditions for an algebra in a rigid monoidal category to be Frobenius in terms of the existence of categorical Frobenius form. These two results of independent interest are used to achieve our goal. As an application of our main result, we show that any exact module category over a symmetric finite tensor category is represented by a Frobenius algebra in it. This is joint work with Dr. Chelsea Walton (Rice University).