Let be a fusion category faithfully graded by a finite group and let be the trivial component of this grading. The center of is shown to be canonically equivalent to a -equivariantization of the relative center . We use this result to obtain a criterion for to be group-theoretical and apply it to Tambara–Yamagami fusion categories. We also find several new series of modular categories by analyzing the centers of Tambara–Yamagami categories. Finally, we prove a general result about the existence of zeroes in -matrices of weakly integral modular categories.
"Centers of graded fusion categories." Algebra Number Theory 3 (8) 959 - 990, 2009. https://doi.org/10.2140/ant.2009.3.959