A theory of Galois co-objects for von Neumann bialgebras is introduced. This concept is closely related to the notion of comonoidal W*-Morita equivalence between von Neumann bialgebras, which is a Morita equivalence taking the comultiplication structure into account. We show that the property of ‘being a von Neumann algebraic quantum group’ (i.e. ‘having invariant weights’) is preserved under this equivalence relation. We also introduce the notion of a projective corepresentation for a von Neumann bialgebra, and show how it leads to a construction method for Galois co-objects and comonoidal W*-Morita equivalences.
Cite this article
Kenny De Commer, Comonoidal W*-Morita equivalence for von Neumann bialgebras. J. Noncommut. Geom. 5 (2011), no. 4, pp. 547–571DOI 10.4171/JNCG/86