$G$-crossed braided zesting Institutional Repository Document uri icon

abstract

  • For a finite group $G$, a $G$-crossed braided fusion category is $G$-graded fusion category with additional structures, namely a $G$-action and a $G$-braiding. We develop the notion of $G$-crossed braided zesting: an explicit method for constructing new $G$-crossed braided fusion categories from a given one by means of cohomological data associated with the invertible objects in the category and grading group $G$. This is achieved by adapting a similar construction for (braided) fusion categories recently described by the authors. All $G$-crossed braided zestings of a given category $mathcal{C}$ are $G$-extensions of their trivial component and can be interpreted in terms of the homotopy-based description of Etingof, Nikshych and Ostrik. In particular, we explicitly describe which $G$-extensions correspond to $G$-crossed braided zestings.

author list (cited authors)

  • Delaney, C., Galindo, C., Plavnik, J., Rowell, E., & Zhang, Q.

citation count

  • 0

complete list of authors

  • Delaney, Colleen||Galindo, C├ęsar||Plavnik, Julia||Rowell, Eric||Zhang, Qing

Book Title

  • arXiv

publication date

  • December 2022