Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 13 (2017), 042, 9 pages      arXiv:1608.04435      https://doi.org/10.3842/SIGMA.2017.042

On the Equivalence of Module Categories over a Group-Theoretical Fusion Category

Sonia Natale
Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba, CIEM-CONICET, Córdoba, Argentina

Received April 28, 2017, in final form June 14, 2017; Published online June 17, 2017

Abstract
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. This concludes the classification of such module categories.

Key words: fusion category; module category; group-theoretical fusion category.

pdf (347 kb)   tex (14 kb)

References

  1. Etingof P., Gelaki S., Nikshych D., Ostrik V., Tensor categories, Mathematical Surveys and Monographs, Vol. 205, Amer. Math. Soc., Providence, RI, 2015.
  2. Marshall I., Nikshych D., On the Brauer-Picard groups of fusion categories, Math. Z., to appear, arXiv:1603.04318.
  3. Masuoka A., Semisimple Hopf algebras of dimension $6$, $8$, Israel J. Math. 92 (1995), 361-373.
  4. 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), Contemp. Math., Vol. 267, Amer. Math. Soc., Providence, RI, 2000, 195-214.
  5. Naidu D., Crossed pointed categories and their equivariantizations, Pacific J. Math. 247 (2010), 477-496, arXiv:1111.5246.
  6. Natale S., On group theoretical Hopf algebras and exact factorizations of finite groups, J. Algebra 270 (2003), 199-211, math.QA/0208054.
  7. Nikshych D., Non-group-theoretical semisimple Hopf algebras from group actions on fusion categories, Selecta Math. (N.S.) 14 (2008), 145-161, arXiv:0712.0585.
  8. Ostrik V., Module categories over the Drinfeld double of a finite group, Int. Math. Res. Not. 2003 (2003), 1507-1520, math.QA/0202130.
  9. Schauenburg P., Hopf bimodules, coquasibialgebras, and an exact sequence of Kac, Adv. Math. 165 (2002), 194-263.

Previous article  Next article   Contents of Volume 13 (2017)