Deformations of Frobenius algebras and noncommutative 2d topological quantum field theories

Abstract: In this talk I will present an attempt to define noncommutative 2d topological quantum field theories using deformations of Frobenius algebras. First, we will overview the importance and uses of 2d topological quantum field theories, as well as their equivalence to commutative Frobenius algebras. Then, we will consider the deformations given by cotwisted tensor products, characterize when these are Frobenius algebras, and explain their deficiencies for our goal. Afterwards, I will introduce the notion of warped tensor products of Frobenius algebras and characterize when these are Frobenius algebras. This notion enables us to construct a family of bifunctors that could potentially yield nonsymmetric monoidal structures on the category of Frobenius algebras, which would then deserve to be called noncommutative 2d topological quantum field theories. This is work in progress with Rohan Das and Julia Plavnik.

combinatoricsquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

OIST representation theory seminar

Series comments: Timings of this seminar may vary from week to week.