compact quantum group
Definition 0.1.
A compact quantum group, QCG is defined as a particular case of a locally compact quantum group QLCG, that is, a quadruple (A,Δ,μ,ν), where A is either a C*– or a
W*– algebra
equipped with a co-associative comultiplication (http://planetmath.org/WeakHopfCAlgebra2)
Δ:A→A⊗A, and two faithful
semi-finite normal weights, μ and ν –right and -left Haar measures, and also when the object space 𝐎 of the latter QLCG is replaced by a compact topological space QTCG, instead of being a locally compact topological space like QLCG.
References
- 1 A. Maes, and A. VanDaele. 1998. http://arxiv.org/PS_cache/math/pdf/9803/9803122v1.pdfNotes on Compact Quantum Groups., arxiv.org.math-FA-9803122v1, 43 pp.
Title | compact quantum group |
Canonical name | CompactQuantumGroup |
Date of creation | 2013-03-22 18:24:07 |
Last modified on | 2013-03-22 18:24:07 |
Owner | bci1 (20947) |
Last modified by | bci1 (20947) |
Numerical id | 25 |
Author | bci1 (20947) |
Entry type | Definition |
Classification | msc 81R15 |
Classification | msc 81R50 |
Classification | msc 46L05 |
Synonym | quantum group |
Synonym | compact matrix quantum group |
Related topic | CAlgebra3 |
Related topic | QuantumOperatorAlgebrasInQuantumFieldTheories |
Related topic | FiniteQuantumGroup |
Related topic | DualityInMathematics |
Related topic | LocallyCompactQuantumGroup |
Related topic | QuantumGroups |
Related topic | GelfandTransform |