A Geometric Construction for Permutation Equivariant Categories from Modular Functors
Quantum Algebra
2015-03-14 v2 Category Theory
Abstract
Let G be a finite group. Given a finite G-set X and a modular tensor category C, we construct a weak G-equivariant fusion category, called the permutation equivariant tensor category. The construction is geometric and uses the formalism of modular functors. As an application, we concretely work out a complete set of structure morphisms for Z/2-permutation equivariant categories, finishing thereby a program we initiated in an earlier paper arXiv:0812.0986 [math.CT].
Cite
@article{arxiv.1004.1825,
title = {A Geometric Construction for Permutation Equivariant Categories from Modular Functors},
author = {Till Barmeier and Christoph Schweigert},
journal= {arXiv preprint arXiv:1004.1825},
year = {2015}
}
Comments
64 pages, many figures. v2: minor changes, typos corrected; extended version of text to be published in Transformation Groups