English

Gauge invariants from the powers of antipodes

Quantum Algebra 2017-09-25 v3

Abstract

We prove that the trace of the nnth power of the antipode of a Hopf algebra with the Chevalley property is a gauge invariant, for each integer nn. 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.

Keywords

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