Amenability and co-amenability of algebraic quantum groups

Details Amenability and co-amenability of algebraic quantum groups Amenability and co-amenability of algebraic quantum groups

2001-11-02

arxiv.org/abs/math/0111025v2

Mathematics

Operator Algebras

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

Scientific paper

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.

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