Quantum \(SU(2)\) and \(E(2)\) groups. Contraction procedure
type: Item
instance of: scholarly article
title: Quantum \(SU(2)\) and \(E(2)\) groups. Contraction procedure
zbMATH Open document ID: 0759.17009
DOI: 10.1007/BF02096947
published in: Communications in Mathematical Physics
publication date: 1993-01-17T00:00:00Z
review text: The author shows how the contraction procedure works in the theory of topological quantum groups. He considers the problem that quantum \(SU(2)\) and \(E(2)\) groups are related by contraction procedure on the \(C^*\)- level. In particular, he finds a number of formulae relating the comultiplications in quantum \(SU(2)\) and \(E(2)\) groups, and shows that the comultiplications in both groups are implemented by partial isometries. In addition, the author discovers an unexpected feature of quantum \(E(2)\) and describes the corresponding strange behavior of quantum \(SU(2)\). It turns out that in certain aspects they behave like locally compact semigroups.
reviewed by: Ye Jiachen
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 22A15
Mathematics Subject Classification ID: 46L89
zbMATH DE Number: 97878
zbMATH Keywords: quantum \(E(2)\)
zbMATH Keywords: quantum \(SU(2)\)
zbMATH Keywords: contraction procedure
zbMATH Keywords: topological quantum groups
zbMATH Keywords: locally compact semigroups
author: Stanisław Lech Woronowicz
MaRDI profile type: Publication
cites work: Q3344718
cites work: Q3924413
cites work: Three-dimensional quantum groups from contractions of SU(2)q
cites work: The quantum Heisenberg group H(1)q
cites work: The three-dimensional Euclidean quantum group E(3)q and its R-matrix
cites work: On the Contraction of Groups and Their Representations
cites work: Q4765335
cites work: Q3205815
cites work: Quantum spheres
cites work: Quantum deformation of Lorentz group
cites work: C* -Algèbres de Hopf et C* -Algèbres de Kac
cites work: Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
cites work: Unbounded elements affiliated with \(C^*\)-algebras and non-compact quantum groups
cites work: Operator equalities related to the quantum \(E(2)\) group
cites work: Quantum \(E(2)\) group and its Pontryagin dual
full work available at URL: https://doi.org/10.1007/bf02096947
OpenAlex ID: W2051157853
description: scientific article; zbMATH DE number 97878