Gauge invariants from the powers of antipodes
Quantum Algebra
2017-09-25 v3
Abstract
We prove that the trace of the th power of the antipode of a Hopf algebra with the Chevalley property is a gauge invariant, for each integer . As a consequence, the order of the antipode, and its square, are invariant under Drinfeld twists. The invariance of the order of the antipode is closely related to a question of Shimizu on the pivotal covers of finite tensor categories, which we affirmatively answer for representation categories of Hopf algebras with the Chevalley property.
Cite
@article{arxiv.1609.00994,
title = {Gauge invariants from the powers of antipodes},
author = {Cris Negron and Siu-Hung Ng},
journal= {arXiv preprint arXiv:1609.00994},
year = {2017}
}
Comments
20 pages latex, minor typo corrections of the previous version