Frobenius algebras and homotopy fixed points of group actions on bicategories

TL;DR

This paper establishes a bijection between symmetric Frobenius structures on finite-dimensional semi-simple algebras and homotopy fixed points of an SO(2) action on a bicategory, linking algebraic structures to topological quantum field theory.

Contribution

It explicitly connects Frobenius algebra structures with homotopy fixed points in bicategories, motivated by the 2D Cobordism Hypothesis and TQFT.

Findings

Bijection between Frobenius structures and homotopy fixed points.

Application to 2D Topological Quantum Field Theory.

Insights into algebraic structures via bicategory actions.

Abstract

We explicitly show that symmetric Frobenius structures on a finite-dimensional, semi-simple algebra stand in bijection to homotopy fixed points of the trivial SO(2)-action on the bicategory of finite-dimensional, semi-simple algebras, bimodules and intertwiners. The results are motivated by the 2-dimensional Cobordism Hypothesis for oriented manifolds, and can hence be interpreted in the realm of Topological Quantum Field Theory.