Bar categories and star operations
type: Item
instance of: scholarly article
title: Bar categories and star operations
zbMATH Open document ID: 1180.18002
author: Shahn Majid
author: Edwin Beggs
published in: Algebras and Representation Theory
publication date: 2009-09-01T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0701008
review text: The category of complex vector spaces admits an involutive endofunctor taking each vector space to itself with conjugate scalar multiplication. The bar categories defined here abstract this to a pseudo-involutive endofunctor on a monoidal category; there are some more isomorphisms and some axioms. Categories of modules (or comodules) over a star-Hopf algebra are clear examples; but there are others involving flip-star-, and quasi-star-Hopf algebras. A Tannaka-like result reconstructs a star-Hopf algebra from a (strong) bar category with appropriate fibre functor.
Mathematics Subject Classification ID: 18D10
Mathematics Subject Classification ID: 46L87
Mathematics Subject Classification ID: 58B32
Mathematics Subject Classification ID: 16T05
Mathematics Subject Classification ID: 81R50
zbMATH DE Number: 5600710
zbMATH Keywords: monoidal category
zbMATH Keywords: tensor category
zbMATH Keywords: Hopf algebra
zbMATH Keywords: Tannaka reconstruction
zbMATH Keywords: conjugate scalar multiplication
reviewed by: Ross H. Street
MaRDI profile type: Publication
OpenAlex ID: W2591735977
arXiv ID: math/0701008
cites work: Quasialgebra structure of the octonions
cites work: Making nontrivially associated modular categories from finite groups
cites work: *-autonomous categories. With an appendix by Po-Hsiang Chu
cites work: Higher-dimensional algebra. II: 2-Hilbert spaces
cites work: Making non-trivially associated tensor categories from left coset representatives
cites work: Nonassociative tori and applications to \(T\)-duality
cites work: Q4310044
cites work: Q5749433
cites work: Braided tensor categories
cites work: Q5639839
cites work: Q4857364
cites work: *-structures on braided spaces
cites work: Quasi-\(*\) structure on \(q\)-Poincaré algebras
cites work: Q4693947
cites work: Modules graded by G-sets
cites work: Graded modules over \(G\)-sets. II
cites work: Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
DOI: 10.1007/S10468-009-9141-X
description: scientific article