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Amenability and coamenability of algebraic quantum groups

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  • Erik Bédos
  • Gerard J. Murphy
  • Lars Tuset

Abstract

We define concepts of amenability and coamenability for algebraic quantum groups in the sense of Van Daele (1998). We show that coamenability of an algebraic quantum group always implies amenability of its dual. Various necessary and/or sufficient conditions for amenability or coamenability are obtained. Coamenability is shown to have interesting consequences for the modular theory in the case that the algebraic quantum group is of compact type.

Suggested Citation

  • Erik Bédos & Gerard J. Murphy & Lars Tuset, 2002. "Amenability and coamenability of algebraic quantum groups," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 31, pages 1-25, January.
    • Handle: RePEc:hin:jijmms:386965
    DOI: 10.1155/S016117120210603X
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