# PlanetPhysics/L Compact Quantum Groups

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Definition 0.1

A *locally compact quantum group* defined as in ref. ^{[1]} is a quadruple , where is either a - or a
- algebra equipped with a co-associative comultiplication
and two faithful semi-finite normal weights,
and - right and -left Haar measures.

**Examples**

- An ordinary unimodular group with Haar measure :

, , where .

- A = \L (G) is the von Neumann algebra generated by left-translations or by left convolutions with continuous functions , where , and is the unit of .

## All SourcesEdit

^{[1]}

## ReferencesEdit

- ↑
^{1.0}^{1.1}Leonid Vainerman. 2003.*Locally Compact Quantum Groups and Groupoids:*Proceedings of the Meeting of Theoretical Physicists and Mathematicians, Strasbourg, February 21-23, 2002*Series in Mathematics and Theoretical Physics*,**2**, Series ed. V. Turaev., Walter de Gruyter Gmbh et Co: Berlin.