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We give a necessary and sufficient condition in terms of group cohomology for two indecomposable module categories over a group-theoretical fusion category ${\mathcal C}$ to be equivalent.
Masuoka A., Semisimple Hopf algebras of dimension
1995
Earlier work this paper cites.
Masuoka A., Cocycle deformations and Galois objects for some cosemisimple Hopf algebras of finite dimension, in New Trends in Hopf Algebra Theory (La Falda, 1999),
2000
Earlier work this paper cites.
Schauenburg P., Hopf bimodules, coquasibialgebras, and an exact sequence of Kac,
2002
Earlier work this paper cites.
Natale S., On group theoretical Hopf algebras and exact factorizations of finite groups,
2003
Cited alongside, same era.
Ostrik V., Module categories over the Drinfeld double of a finite group,
2003
Cited alongside, same era.
Nikshych D., Non-group-theoretical semisimple Hopf algebras from group actions on fusion categories,
2008
Cited alongside, same era.
Marshall I., Nikshych D., On the Brauer–Picard groups of fusion categories,
Cited in the paper.
Naidu D., Crossed pointed categories and their equivariantizations,
2010
Later among the works it cites.
Etingof P., Gelaki S., Nikshych D., Ostrik V., Tensor categories,
2015
Later among the works it cites.
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