locally compact quantum group
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 = Ł(G) is the von Neumann algebra
generated by left-translations
or by left convolutions
with continuous functions
, where
, and
is the unit of
.
-
- 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.
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