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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.
@article{TAC_2017_32_a17,
author = {Jan Hesse and Christoph Schweigert and Alessandro Valentino},
title = {Frobenius algebras and homotopy fixed points of group actions on bicategories},
journal = {Theory and applications of categories},
pages = {652--681},
publisher = {mathdoc},
volume = {32},
year = {2017},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a17/}
}
TY - JOUR AU - Jan Hesse AU - Christoph Schweigert AU - Alessandro Valentino TI - Frobenius algebras and homotopy fixed points of group actions on bicategories JO - Theory and applications of categories PY - 2017 SP - 652 EP - 681 VL - 32 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TAC_2017_32_a17/ LA - en ID - TAC_2017_32_a17 ER -
%0 Journal Article %A Jan Hesse %A Christoph Schweigert %A Alessandro Valentino %T Frobenius algebras and homotopy fixed points of group actions on bicategories %J Theory and applications of categories %D 2017 %P 652-681 %V 32 %I mathdoc %U http://geodesic.mathdoc.fr/item/TAC_2017_32_a17/ %G en %F TAC_2017_32_a17
Jan Hesse; Christoph Schweigert; Alessandro Valentino. Frobenius algebras and homotopy fixed points of group actions on bicategories. Theory and applications of categories, Tome 32 (2017), pp. 652-681. http://geodesic.mathdoc.fr/item/TAC_2017_32_a17/