English

On the graded center of graded categories

Quantum Algebra 2012-08-29 v1 Category Theory

Abstract

We study the G-centers of G-graded monoidal categories where G is an arbitrary group. We prove that for any spherical G-fusion category C over an algebraically closed field such that the dimension of the neutral component of C is non-zero, the G-center of C is a G-modular category. This generalizes a theorem of M. M\"uger corresponding to G=1. We also exhibit interesting objects of the G-center.

Keywords

Cite

@article{arxiv.1208.5696,
  title  = {On the graded center of graded categories},
  author = {Vladimir Turaev and Alexis Virelizier},
  journal= {arXiv preprint arXiv:1208.5696},
  year   = {2012}
}