arXiv subjects

E. Bedos

Publications and source records attributed to E. Bedos.

3 recordsLinked to original sources

arXiv2002

Amenability and co-amenability of algebraic quantum groups

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.

math.OA↗

arXiv2001

On amenability and co-amenability of algebraic quantum groups and their corepresentations

We introduce and study several amenability properties for unitary corepresentations and *-representations of algebraic quantum groups, which may be used to characterize amenability or co-amenability of such groups. As a background for this study, we also investigate the involved tensor C*-categories.

math.OA↗

arXiv2001

Amenability and co-amenability of algebraic quantum groups II

We continue our study of the concepts of amenability and co-amenability for algebraic quantum groups in the sense of A. Van Daele and our investigation of their relationship with nuclearity and injectivity. One major tool for our analysis is that every non-degenerate *-representation of the universal C*-algebra associated to an algebraic quantum qroup has a unitary generator which may be described in a concrete way.

math.OA↗