HOPF ALGEBRA ACTIONS IN TENSOR CATEGORIES

Autor:	Marcel Bischoff, Alexei Davydov
Rok vydání:	2020
Předmět:	Pure mathematics FOS: Physical sciences 01 natural sciences Group action Mathematics::Category Theory Tensor (intrinsic definition) Mathematics - Quantum Algebra 0103 physical sciences FOS: Mathematics Quantum Algebra (math.QA) Category Theory (math.CT) 0101 mathematics Algebra over a field Representation (mathematics) Commutative property Mathematical Physics Mathematics Algebra and Number Theory Group (mathematics) 010102 general mathematics Mathematics - Category Theory Mathematical Physics (math-ph) 16. Peace & justice Hopf algebra Action (physics) 010307 mathematical physics Geometry and Topology
Zdroj:	Transformation Groups. 26:69-80
ISSN:	1531-586X 1083-4362
DOI:	10.1007/s00031-020-09560-w
Popis:	We prove that commutative algebras in braided tensor categories do not admit faithful Hopf algebra actions unless they come from group actions. We also show that a group action allows us to see the algebra as the regular algebra in the representation category of the acting group. Comment: 8pages, several figures. v2 minor changes. As sent for publication to Transformation Groups
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::97ec028b9e4dd4c7789ddee1885f1a3a https://doi.org/10.1007/s00031-020-09560-w Zobrazit plný text záznamu Full text from SpringerLink