Quantum symmetry groups and related topics
type: Item
instance of: scholarly article
title: Quantum symmetry groups and related topics
zbMATH Open document ID: 1395.81121
DOI: 10.1007/978-3-319-63206-3_3
publication date: 2018-03-06T00:00:00Z
review text: In hindsight one can define the symmetry groups acting on \(X\) (in a manner preserving the relevant features of \(X\)). These form a category, and the symmetry group of \(X\), say \(\mathrm{Sym}_X\) is a universal object of this category. Thus \(\mathrm{Sym}_X\) is a group acting on \(X\) and every action of a group \(G\) on \(X\) can be viewed simply as a homomorphism from \(G\) to \(\mathrm{Sym}_X\). Here the notion of individual, point transformations will be absent and the categorical approach will be useful. The author works with quantum symmetries of finite or compact structures. The theory is based on actions of compact quantum groups on \(C^\ast\)-algebras. The aim is to present old and new research developments, discussing both the general theory and specific examples. At the end, a list of open problems is given. For the entire collection see [Zbl 1381.81011].
reviewed by: Gabriela Paola Ovando
Mathematics Subject Classification ID: 81R05
Mathematics Subject Classification ID: 22E70
Mathematics Subject Classification ID: 81R50
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 46L60
zbMATH DE Number: 6847383
zbMATH Keywords: quantum symmetry groups
zbMATH Keywords: actions of quantum groups
zbMATH Keywords: \(C^\ast\)-algebras
author: Adam Skalski
MaRDI profile type: Publication
full work available at URL: 978-3-319-63206-3 3
OpenAlex ID: W2762224673
description: scientific article; zbMATH DE number 6847383