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Title: G ‐crossed braided zesting
Abstract For a finite group , a ‐crossed braided fusion category is a ‐graded fusion category with additional structures, namely, a ‐action and a ‐braiding. We develop the notion of ‐crossed braided zesting: an explicit method for constructing new ‐crossed braided fusion categories from a given one by means of cohomological data associated with the invertible objects in the category and grading group . This is achieved by adapting a similar construction for (braided) fusion categories recently described by the authors. All ‐crossed braided zestings of a given category are ‐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 ‐extensions correspond to ‐crossed braided zestings.  more » « less
Award ID(s):
2205962 2000331 2146392
PAR ID:
10469851
Author(s) / Creator(s):
 ;  ;  ;  ;  
Publisher / Repository:
Oxford University Press (OUP)
Date Published:
Journal Name:
Journal of the London Mathematical Society
Volume:
109
Issue:
1
ISSN:
0024-6107
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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