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

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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.
46 pages, (some misprints corrected, a couple of remarks and a new reference added)

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