Amenability and co-amenability of algebraic quantum groups

Abstract

We define concepts of amenability and co-amenability for algebraic quantum groups in the sense of A. Van Daele. We show that co-amenability of an algebraic quantum group always implies amenability of its dual. Various necessary and/or sufficient conditions for amenability or co-amenability are obtained. Co-amenability is shown to have interesting consequences for the modular theory in the case that the algebraic quantum group is of compact type.

25 pages, with some minor corrections, as to appear in the IJMMS

References in corpus (7)

• Co-Amenability of compact quantum groups
• Fusion rules for representations of compact quantum groups
• One-parameter representations on C*-algebras
• Amenability of Hopf C^*-algebras
• Universal C*-algebraic quantum groups arising from algebraic quantum groups
• The analytic structure of an algebraic quantum group
• Amenability and co-amenability of algebraic quantum groups II

Cited by in corpus (1)

• Amenability and co-amenability of algebraic quantum groups II