Weight theory for C*-algebraic quantum groups

Abstract

In this paper, we collect some technical results about weights on C*-algebras which are useful in de theory of locally compact quantum groups in the C*-algebra framework. We discuss the extension of a lower semi-continuous weight to a normal weight following S. Baaj, look into slice weights and their KSGNS-constructions and investigate the tensor product of weights together with a partial GNS-construction for such a tensor product. This paper accompanies our paper 'Locally compact quantum groups' in which we propose a relatively simple definition of a locally compact quantum group in the C*-algebra framework.

46 pages, LaTeX

References in corpus (4)

• KMS-weights on C*-algebras
• One-parameter representations on C*-algebras
• Regular C*-valued weights
• The functional calculus for regular operators in Hilbert C*-modules revisited

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• KMS weights on groupoid and graph C*-algebras
• KMS weights on graph C*-algebras II Factor types and ground states
• A class of C*-algebraic locally compact quantum groupoids Part II: Main theory
• A generalized Fourier inversion theorem
• Generalized fixed point algebras for coactions of locally compact quantum groups
• Construction of a $C^{\ast }$-algebraic quantum groupoid from a weak multiplier Hopf algebra
• Induced corepresentations of locally compact quantum groups