All Questions
8 questions
18
votes
0
answers
557
views
Do quotients of amenable groups C*-algebras satisfy the UCT?
Let G be a discrete amenable group.
General Question: Let $J$ be an ideal of $C^*(G)$, the group C*-algebra of $G.$ Does $C^*(G)/J$ satisfy the universal
coefficient theorem (UCT)?
I am mainly ...
- 2,689
10
votes
1
answer
283
views
Faithful extreme traces on group C*-algebras
Let $G$ be a discrete amenable, residually finite, ICC(i.e. each non-trivial conjugacy class is infinite) group. Let $C^*_r(G)$ be the reduced group $C^*$-algebra of $G$. Since $G$ is ICC the (...
- 2,689
9
votes
0
answers
483
views
The approximation property of group C*-algebras
Let $G$ be a discrete group. Then the group C*-algebra $C^*(G)$ is nuclear if and only if $G$ is amenable. I am wondering whether nuclearity of $C^*(G)$ can fail for a Banach-space reason, namely due ...
- 11.3k
7
votes
2
answers
871
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
7
votes
0
answers
573
views
References for "folklore" on strong amenability of (group) C*-algebras?
[Apologies in advance for the prolixity - but I was unsure how much of the story is familiar.]
$\newcommand{\ptp}{\widehat{\otimes}}
\newcommand{\co}{\operatorname{co}}
\newcommand{\Cst}{\operatorname{...
- 25.8k
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
5
votes
1
answer
287
views
example of a non-amenable l.c. group such that $C_r^*(G)$ satisfies the UCT
Are there known any examples of non-amenable locally compact (or more restrictive, non-amenable discrete) groups $G$ for which the reduced group $C^*$-algebra $C_r^*(G)$ satisfies the universal ...
user62639
2
votes
0
answers
100
views
Amenability for Actions twited with 2-cocycles
Let $A \subset B(H)$ be a unital $C^\ast$-algebra and $\theta: G \rightarrow \mathrm{Aut}(A)$ an action and let $\omega: G \times G \rightarrow U(\mathcal{Z}(A))$ be a $2$-cocyle with respect to $\...
- 1,090