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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 .
- ↑ 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.