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Title: On the Grothendieck rings of equivariant fusion categories

Abstract

In this paper, we describe a Mackey type decomposition for group actions on abelian categories. This allows us to define new Mackey functors which associates to any subgroup the K-theory of the corresponding equivariantized abelian category. In the case of an action by tensor autoequivalences, the Mackey functor at the level of Grothendieck rings has a Green functor structure. As an application we give a description of the Grothendieck rings of equivariantized fusion categories under group actions by tensor autoequivalences on graded fusion categories. In this settings, a new formula for the tensor product of any two simple objects of an equivariantized fusion category is given, simplifying the fusion formula from Burciu and Natale [J. Math. Phys. 54, 013511 (2013)].

Authors:
 [1]
  1. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, Research Unit 5, P.O. Box 1-764, RO-014700 Bucharest (Romania)
Publication Date:
OSTI Identifier:
22479695
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 56; Journal Issue: 7; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; FUNCTIONS; GROUP THEORY; TENSORS

Citation Formats

Burciu, Sebastian. On the Grothendieck rings of equivariant fusion categories. United States: N. p., 2015. Web. doi:10.1063/1.4926949.
Burciu, Sebastian. On the Grothendieck rings of equivariant fusion categories. United States. https://doi.org/10.1063/1.4926949
Burciu, Sebastian. 2015. "On the Grothendieck rings of equivariant fusion categories". United States. https://doi.org/10.1063/1.4926949.
@article{osti_22479695,
title = {On the Grothendieck rings of equivariant fusion categories},
author = {Burciu, Sebastian},
abstractNote = {In this paper, we describe a Mackey type decomposition for group actions on abelian categories. This allows us to define new Mackey functors which associates to any subgroup the K-theory of the corresponding equivariantized abelian category. In the case of an action by tensor autoequivalences, the Mackey functor at the level of Grothendieck rings has a Green functor structure. As an application we give a description of the Grothendieck rings of equivariantized fusion categories under group actions by tensor autoequivalences on graded fusion categories. In this settings, a new formula for the tensor product of any two simple objects of an equivariantized fusion category is given, simplifying the fusion formula from Burciu and Natale [J. Math. Phys. 54, 013511 (2013)].},
doi = {10.1063/1.4926949},
url = {https://www.osti.gov/biblio/22479695}, journal = {Journal of Mathematical Physics},
issn = {0022-2488},
number = 7,
volume = 56,
place = {United States},
year = {Wed Jul 15 00:00:00 EDT 2015},
month = {Wed Jul 15 00:00:00 EDT 2015}
}