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 .