Duals of quantum semigroups with involution
Résumé
We define a category QSI of quantum semigroups with involution which carries a corepresentation-based duality map M → M. Objects in QSI are von Neumann algebras with comultiplication and coinvolution, we do not suppose the existence of a Haar weight or of a distinguished spatial realisation. In the case of a locally compact quantum group G, the duality in QSI recovers the universal duality of Kustermans: L ∞ (G) = C u 0 (G) * * = C u 0 (G) * * , and L ∞ (G) = C u 0 (G) * * = C u 0 (G) * *. Other various examples are given.
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