Higher Frobenius-Schur Indicators for Pivotal Categories
Quantum Algebra
2015-11-13 v2 Category Theory
Abstract
We define higher Frobenius-Schur indicators for objects in linear pivotal monoidal categories. We prove that they are category invariants, and take values in the cyclotomic integers. We also define a family of natural endomorphisms of the identity endofunctor on a -linear semisimple rigid monoidal category, which we call the Frobenius-Schur endomorphisms. For a -linear semisimple pivotal monoidal category -- where both notions are defined --, the Frobenius-Schur indicators can be computed as traces of the Frobenius-Schur endomorphisms.
Cite
@article{arxiv.math/0503167,
title = {Higher Frobenius-Schur Indicators for Pivotal Categories},
author = {Siu-Hung Ng and Peter Schauenburg},
journal= {arXiv preprint arXiv:math/0503167},
year = {2015}
}
Comments
A paragraph which describes the organization of the paper has been added to the introduction. Some observations have been added to Theorems 5.1 and 7.6