compact quantum group

Definition 0.1.

A compact quantum group, $Q_{CG}$ is defined as a particular case of a locally compact quantum group $Q_{LCG}$ , that is, a quadruple $(A,\\Delta,\\mu,\u)$ , where $A$ is either a $C^{*}$ – or a $W^{*}$ – algebra equipped with a co-associative comultiplication (http://planetmath.org/WeakHopfCAlgebra2) $\\Delta:A\\to A\\otimes A$ , and two faithful semi-finite normal weights, $\\mu$ and $\u$ –right and -left Haar measures, and also when the object space $\\mathbf{O}$ of the latter $Q_{LCG}$ is replaced by a compact topological space $Q^{T}_{CG}$ , instead of being a locally compact topological space like $Q_{LCG}$ .

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.

单词	CompactQuantumGroup
释义	compact quantum group Definition 0.1. A compact quantum group, $Q_{CG}$ is defined as a particular case of a locally compact quantum group $Q_{LCG}$ , that is, a quadruple $(A,\\Delta,\\mu,\u)$ , where $A$ is either a $C^{}$ – or a $W^{}$ – algebra equipped with a co-associative comultiplication (http://planetmath.org/WeakHopfCAlgebra2) $\\Delta:A\\to A\\otimes A$ , and two faithful semi-finite normal weights, $\\mu$ and $\u$ –right and -left Haar measures, and also when the object space $\\mathbf{O}$ of the latter $Q_{LCG}$ is replaced by a compact topological space $Q^{T}_{CG}$ , instead of being a locally compact topological space like $Q_{LCG}$ . 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.
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