Gauge invariants from the powers of antipodes
| Autor: | Cris Negron, Siu-Hung Ng |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Trace (linear algebra) General Mathematics 010102 general mathematics Mathematics::Rings and Algebras Order (ring theory) Gauge (firearms) 16. Peace & justice Hopf algebra 01 natural sciences Square (algebra) Integer Tensor (intrinsic definition) Mathematics::Category Theory Mathematics::Quantum Algebra 0103 physical sciences Mathematics - Quantum Algebra FOS: Mathematics Quantum Algebra (math.QA) 010307 mathematical physics 0101 mathematics Invariant (mathematics) Mathematics |
| Popis: | 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. 20 pages latex, minor typo corrections of the previous version |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|