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.
Keywords: symmetric Frobenius algebras, homotopy fixed points, group actions on bicategories
2010 MSC: 18D05
Theory and Applications of Categories, Vol. 32, 2017, No. 18, pp 652-681.