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)

category theoryquantum algebra

Audience: researchers in the topic

Quantum Groups Seminar [QGS]

Series comments: This seminar aims to bring together experts in the area of quantum groups. The seminar topics will cover the theory of quantum groups and related structures in a large sense: Hopf algebras, operator algebras, q-deformations, higher categories and related branches of noncommutative mathematics.

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