Relative Matched Pairs of Finite Groups from Depth Two Inclusions of Von Neumann Algebras to Quantum Groupoids

Actions and Coactions of Finite Quantum Groupoids on Von Neumann Algebras, Extensions of the Match Pair Procedure

In this work we investigate the notion of action or coaction of a finite quantum groupoid in von Neumann algebras context. In particular we prove a double crossed product theorem and prove the existence of an universal von Neumann algebra on which any finite groupoids acts outerly. In previous works, N. Andruskiewitsch and S.Natale define for any match pair of groupoids two C∗-quantum groupoids...

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

Various topological forms of Von Neumann regularity in Banach algebras

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

Outer Actions of Measured Quantum Groupoids

Mimicking a recent article of Stefaan Vaes, in which was proved that every locally compact quantum group can act outerly, we prove that we get the same result for measured quantum groupoids, with an appropriate definition of outer actions of measured quantum groupoids. This result is used to show that every measured quantum groupoid can be found from some depth 2 inclusion of von Neumann algebras.

INCLUSIONS OF VON NEUMANN ALGEBRAS, AND QUANTUM GROUPOÿIDS II

In a former article, in collaboration with Jean-Michel Vallin, we have constructed two ”quantum groupoÿıds” dual to each other, from a depth 2 inclusion of von Neumann algebras M0 ⊂ M1. We are now investigating in greater details these structures : in the previous article, we had constructed the analog of a co-product, and in this paper, are defined a co-inverse, by making the polar decompositi...