Geodesic
Third cohomology and fusion categories
Homology, homotopy, and applications, Tome 20 (2018) no. 1, pp. 275-302.

Voir la notice de l'article provenant de la source International Press of Boston

It was observed recently that for a fixed finite group $G$, the set of all Drinfeld centres of $G$ twisted by 3-cocycles form a group, the so-called group of modular extensions (of the representation category of $G$), which is isomorphic to the third cohomology group of $G$.We show that for an abelian $G$, pointed twisted Drinfeld centres of $G$ form a subgroup of the group of modular extensions.We identify this subgroup with a group of quadratic extensions containing $G$ as a Lagrangian subgroup, the so-called group of Lagrangian extensions of $G$. We compute the group of Lagrangian extensions, thereby providing an interpretation of the internal structure of the third cohomology group of an abelian $G$ in terms of fusion categories. Our computations also allow us to describe associators of Lagrangian algebra in pointed braided fusion categories.
DOI : 10.4310/HHA.2018.v20.n1.a17
Classification : 18D10, 18G15
Keywords: group cohomology, fusion category, finite group theory 
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Alexei Davydov; Darren A. Simmons. Third cohomology and fusion categories. Homology, homotopy, and applications, Tome 20 (2018) no. 1, pp. 275-302. doi : 10.4310/HHA.2018.v20.n1.a17. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2018.v20.n1.a17/

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