Gauge invariants from the powers of antipodes

Cris Negron and Siu-Hung Ng

Vol. 291 (2017), No. 2, 439–460

DOI: 10.2140/pjm.2017.291.439

Abstract

We prove that the trace of the $n$-th power of the antipode of a Hopf algebra with the Chevalley property is a gauge invariant, for each integer $n$. 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

tensor categories, Hopf algebras, gauge invariants, Frobenius–Schur indicators

Mathematical Subject Classification 2010

Primary: 16G99, 16T05, 18D20

Milestones

Received: 17 October 2016

Revised: 11 April 2017

Accepted: 9 May 2017

Published: 14 September 2017