A Geometric Construction for Permutation Equivariant Categories from Modular Functors

Details A Geometric Construction for Permutation Equivariant Categories from Modular Functors A Geometric Construction for Permutation Equivariant Categories from Modular Functors

2010-04-11

arxiv.org/abs/1004.1825v2

Mathematics

Quantum Algebra

64 pages, many figures. v2: minor changes, typos corrected; extended version of text to be published in Transformation Groups

Scientific paper

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].

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