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A simple definition for locally compact quantum groups

✍ Scribed by Johan Kustermans; Stefaan Vaes

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
511 KB
Volume
328
Category
Article
ISSN
0764-4442

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✦ Synopsis

In this Note we propose a simple definition of a locally compact quantum group in reduced form. By the word "reduced" we mean that we suppose the Haar weight to be faithful, and hence we define in fact arbitrary locally compact quantum groups represented on the L'-space of the Haar weight. We construct the multiplicative unitary associated with our quantum group. We construct the antipode with its polar decomposition, and the modular element. We prove the unicity of the Haar weights, define the dual and prove a Pontryagin duality theorem. 0 AcadCmie des SciencesiElsevier. Paris

Une dhfinition simple des groupes quantiques localement compacts

RCSUmC.

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