Reiter’s Properties for the Actions of Locally Compact Quantum Groups on Von Neumann Algebras

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 ...

Variants of a-T-menability for actions on non-commutative Lp-spaces

We investigate various characterizations of the Haagerup property (H) for a second countable locally compact group G, in terms of orthogonal representations of G on Lp(M), the non-commutative Lp-space associated with the von Neumann algebra M. For a semi-finite von Neumann algebra M, we introduce a variant of property (H), namely property HLp(M), defined in terms of orthogonal representations o...

Cohomology of Hopf C-algebras and Hopf von Neumann algebras

We will define two canonical cohomology theories for Hopf C∗-algebras and for Hopf von Neumann algebras (with coefficients in their comodules). We will then study the situations when these cohomologies vanish. The cases of locally compact groups and compact quantum groups will be considered in more details. 1991 AMS Mathematics Classification number: Primary: 46L55, 46L05; Secondary: 43A07, 22D25

Ergodic Actions of Universal Quantum Groups on Operator Algebras

We construct ergodic actions of compact quantum groups on C∗-algebras and von Neumann algebras, and exhibit phenomena of such actions that are of different nature from ergodic actions of compact groups. In particular, we construct: (1). an ergodic action of the compact quantum Au(Q) on the type IIIλ Powers factor Rλ for an appropriate positive Q ∈ GL(2, R); (2). an ergodic action of the compact...