Frobenius algebras and homotopy fixed points of group actions on bicategories

Jan Hesse, Christoph Schweigert, and Alessandro Valentino

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.

Published 2017-05-03.

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