All Questions
8 questions
7
votes
1
answer
306
views
Trans-amenability of group actions
This problem is derived from this post.
Let $G$ be a countable discrete group and $H\le G$ be a subgroup. Consider the $G$-action on $X=G/H$. Then the following amenability-like conditions are ...
- 10.1k
7
votes
2
answers
869
views
Amenable action intuition
Let $\Gamma$ be a discrete group and $A$ be a $C^*$-algebra. Consider an action $\alpha: \Gamma \to \operatorname{Aut}(A)$. There is a notion of amenability for such an action (see e.g. Brown and ...
- 175
6
votes
2
answers
874
views
Is the set of all ICC amenable groups countable?
Is the set of all ICC amenable groups countable?
If "yes", then in general, the classes of all countable ICC groups that give rise to the same von Neumann algebra (factor) -- are these ...
- 121
4
votes
1
answer
212
views
Kernels of representations of $C^*(G)$
Let G be a discrete group. I am interested in the following: let $\pi$ and $\rho$ be two representations of $G$. Denote by $C^*Ker\pi$ and $C^* Ker \rho$ the kernels of the corresponding ...
- 631
6
votes
0
answers
453
views
Does the Approximation Property (AP) pass to quotients by amenable subgroups?
Given a countable group $G$ with the AP, and an normal, amenable subgroup $N$ of $G$, does $G/N$ have the AP?
In particular, does there exist a group $G$ with the AP and a surjective group ...
- 3,497
5
votes
1
answer
622
views
Can the full and reduced group $C^*$-algebras be "noncanonically" isomorphic?
Is there a locally compact group $G$ such that the canonical map from $C^{*}(G)$ to $C^{*}_{red} G$ is not isomorphism, hence $G$ is not amenable but these two $C^{*}$ algebras are isomorphic ...
- 356
1
vote
1
answer
190
views
Infinite amenable group subfactors
Let amenable groups $\Gamma$ and $\Gamma'$. They act outerly of only one manner on the hyperfinite ${\rm II}_1$-factor $\mathcal{R}$.
Question: $(\mathcal{R} \subset \mathcal{R} \rtimes \Gamma) ...
15
votes
1
answer
686
views
Amenability of groups in terms of a perturbation condition
Let $G$ be a countable group and $\lambda \colon G \to U(\ell^2 G)$ its left-regular representation. Suppose that there exists a constant $C>0$ such that for all $T \in B(\ell^2 G)$
$$\inf \lbrace\...
- 25.5k