On the trace of the antipode and higher indicators
Abstract
We introduce two kinds of gauge invariants for any finite-dimensional Hopf algebra H. When H is semisimple over C, these invariants are respectively, the trace of the map induced by the antipode on the endomorphism ring of a self-dual simple module, and the higher Frobenius-Schur indicators of the regular representation. We further study the values of these higher indicators in the context of complex semisimple quasi-Hopf algebras H. We prove that these indicators are non-negative provided the module category over H is modular, and that for a prime p, the p-th indicator is equal to 1 if, and only if, p is a factor of dim H. As an application, we show the existence of a non-trivial self-dual simple H-module with bounded dimension which is determined by the value of the second indicator.
Keywords
Cite
@article{arxiv.0910.1628,
title = {On the trace of the antipode and higher indicators},
author = {Yevgenia Kashina and Susan Montgomery and Siu-Hung Ng},
journal= {arXiv preprint arXiv:0910.1628},
year = {2015}
}
Comments
additional references, fixed some typos, minor additions including a questions and some remarks