7,594 reputation
2442
bio website www2.unine.ch/alain.valette
location Neuchâtel, Switzerland
age 56
visits member for 4 years
seen 3 hours ago

3h
answered Irreducible representation of $C^*(D_\infty)$, group $C^*$-algebra of an infinite dihedral group
9h
comment Using $\mathcal{U(H)}$ as a model for $EG$ and working with the Fredholm Operators
The universal representation $(U_t)$ of the real line is not norm continuous (reason: $\|U_t-1\|=2$ for $t\neq 0$). This should discourage you to use the norm topology on $U(\mathcal{H})$ for your problem.
Apr
21
comment Determining the primitive ideal space of C-star algebras
The example you consider is very special, as it is the $C^*$-algebra of the infinite dihedral group, which is notoriously type I. The spectrum in that case is "an interval with 2+2 endpoints", i.e. the union of two closed intervals identified along their interiors. This well-known fact can be found e.g. in these notes by I. Putnam: math.uvic.ca/faculty/putnam/t/Math_533_Lecture_Notes.pdf
Apr
21
revised “Relative cone types” for groups relative to some collection of subgroups
Fixed spelling
Apr
18
awarded  Yearling
Apr
16
comment Using $\mathcal{U(H)}$ as a model for $EG$ and working with the Fredholm Operators
What are the assumptions on $G$, exactly? And what do you mean by "a/the unitary universe"? Is it the universal representation (so that $G$ is secretly locally compact)?
Mar
19
revised Recollement of multiple $t$-structures
Spelling fixed in title
Mar
13
awarded  Enlightened
Mar
9
comment Product of two foliations
Am I missing something? For question 2, isn't it clear from the definitions that $C^*(F\times F')=C^*(F)\otimes C^*(F')$ (minimal tensor product)?. Think that, if the leaf spaces are Hausdorff, then $C^*(F)$ is Morita equivalent to $C_0(M/F)$, so $C^*(F\times F')$ is Morita equivalent to $C_0((M\times N)/(F\times F'))=C_0(M/F)\otimes C_0(N/F')$.
Feb
7
awarded  Necromancer
Jan
19
comment The kernel of $C^{*}(G)\to C_{r}^{*}(G)$
See "On Isolated Points in the Dual Spaces of Locally Compact Groups", by S. P. Wang, Mathematische Annalen (1975) Volume: 218, page 19-34; available on gdz.sub.uni-goettingen.de/dms/load/img/…
Jan
17
comment The kernel of $C^{*}(G)\to C_{r}^{*}(G)$
This is a wide open question. I personally believe that, for $G$ discrete, the question is intractable, because a description of $I(G)$ is very much related to a description of the dual $\hat{G}$. As an example, consider a residually finite group with property (T). It is known that each finite-dimensional rep is isolated in $\hat{G}$, so defines a direct summand of $C^*(G)$ isomorphic to a matrix algebra. So $I(G)$ contains a huge direct sum of matrix algebras, and probably lots of other stuff too.
Jan
15
comment Embedding Euclidean buildings into products of trees
You're right, I overlooked the surjectivity issue. I leave my comment however, as a very partial contribution.
Jan
15
awarded  Nice Answer
Jan
14
comment Embedding Euclidean buildings into products of trees
I think taking $p=1$ is prevented by the Kleiner-Leeb result on quasi-isometric rigidity of Euclidean buildings: see Theorem 1.1.2 in math.nyu.edu/~bkleiner/symm.pdf
Jan
7
awarded  Enlightened
Jan
7
awarded  Nice Answer
Jan
7
answered Can the full and reduced group $C^*$-algebras be “noncanonically” isomorphic?
Jan
5
comment Are norm-continuous representations smooth?
The 2nd proof is obviously correct, and actually shows that there is a commutative diagram linking $d\rho:\mathfrak{g}\rightarrow A$ and $\rho:G\rightarrow A^{inv}$, where the vertical arrows are given by the exponential maps of $G$ and $A$ respectively.
Jan
5
comment MathScinet reviewing: should I check the proofs?
I think we all agree that, as a reviewer for MR, you're not supposed to check the proofs. Trouble may arise if you find a mathematical mistake in the paper, because you are supposed to explain why it is false, or provide a counter-example, and this can result in painfully long and not so informative reviews.