Related papers: A note on group actions on subfactors
We study equivalence relations and II_1 factors associated with (quotients of) generalized Bernoulli actions of Kazhdan groups. Specific families of these actions are entirely classified up to isomorphism of II_1 factors. This yields…
In this paper, we generalize Izumi's result on uniqueness of realization of finite C$^*$-tensor categories in the endomorphism category of the injective factor of type II_1 for finitely generated strongly amenable C$^*$-tensor categories by…
We study actions of connected algebraic groups on normal algebraic varieties, and show how to reduce them to actions of affine subgroups.
In this note we study countable subgroups of the full group of a measure preserving equivalence relation. We provide various constraints on the group structure, the nature of the action, and on the measure of fixed point sets, that imply…
We consider endomorphism actions of arbitrary discrete semigroups on a connected metrizable topological group G. We give necessary and sufficient conditions for expansiveness of such actions when G is a Lie group or a compact…
We study actions of discrete groups on contractible topological spaces in which either (1) all stabilizers lie in the family of subgroups of prime power order or (2) all stabilizers lie in the family of finite subgroups. We compare the…
Based mainly on examples of interest in mechanics, we define the notion of a polite group action. One may view this as not only trying to give a more general notion than properness of a group action, but also to more fully understand the…
We give the first examples of (non-amenable group) amenable actions on stably finite simple C*-algebras. More precisely, we give such actions for any countable group in an explicit way. The main ingredients of our construction are the full…
We survey some results concerning finite group actions on products of spheres.
We completely characterize connected Lie groups all of whose countable subgroups are weakly amenable. We also provide a characterization of connected semisimple Lie groups that are weakly amenable. Finally, we show that a connected Lie…
We provide a family of group measure space II_1 factors for which all finite index subfactors can be explicitly listed. In particular, the set of all indices of irreducible subfactors can be computed. Concrete examples show that this index…
We show an equivariant Kirchberg-Phillips-type absorption theorem for pointwise outer actions of discrete amenable groups on Kirchberg algebras with respect to natural model actions on the Cuntz algebras $\mathcal{O}_\infty$ and…
We define and study notions of amenability and skew-amenability of continuous actions of topological groups on compact topological spaces. Our main motivation is the question under what conditions amenability of a topological group passes…
P-E. Caprace and N. Monod isolate the class $\mathscr{X}$ of locally compact groups for which relatively amenable closed subgroups are amenable. It is unknown if $\mathscr{X}$ is closed under group extension. In this note, we exhibit a…
We investigate the class of groups admitting an action on a set with an invariant mean. It turns out that many free products admit such an action. We give a complete characterisation of such free products in terms of a strong fixed point…
We develop a cohomology theory of groups based on partial actions and explore its relation with the partial Schur multiplier as well as with cohomology of inverse semigroups.
It is proved that a discrete group G is exact if and only if its left translation action on the Stone-Cech compactification is amenable. Combining this with an unpublished result of Gromov, we have the existence of non exact discrete…
Different notions of amenability on hypergroups and their relations are studied. Developing Leptin's theorem for discrete hypergroups, we characterize the existence of a bounded approximate identity for hypergroup Fourier algebras. We study…
Let G be an infinite discrete countable amenable group acting continuously on a Lebesgue space X. In this article, using partition and factor-space, the conditional entropy of the action G is defined. We introduction some properties of…
We study actions of countable discrete groups which are amenable in the sense that there exists a mean on X which is invariant under the action of G. Assuming that G is nonamenable, we obtain structural results for the stabilizer subgroups…