7,544 reputation
2342
bio website www2.unine.ch/alain.valette
location Neuchâtel, Switzerland
age 56
visits member for 3 years, 11 months
seen 1 hour ago

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.
Jan
5
comment Is there a manifold with fundamental group $\mathbb{Q}$?
@Igor Belegradek: Is an explicit $n$ known?
Jan
5
comment Is this property of the Bell's number evident?
See e.g. that paper for generalizations (and the references within): projecteuclid.org/download/pdf_1/euclid.bbms/1102714984
Jan
3
comment Axiomatic ZFC Set Theory
That's a weird tag...
Jan
3
comment Correspondences as generalized morphism between $C^*$-algebras
Ad Q1: Usually homomorphisms are indeed assumed to be *-homomorphisms. Ad Q2: What about taking for $\phi$ the zero homomorphism $A\rightarrow B$?
Dec
27
answered What is a “Ramanujan Graph”?
Dec
22
comment Murray–von Neumann equivalence on C$^*$-algebra and von Neumann algebra
Sorry you still didn't clarify what you mean by "being a subgroup of $\mathbb{R}$". Remember that, as a consequence of Baum-Connes and the Chern homomorphism, $K_0(A)\otimes\mathbb{Q}$ is $\oplus_{n\geq 0} H_{2n}(\Gamma,\mathbb{Q})$ - and the trace sees only the 0-dimensional part of $K_0$. Although I know of no example, it might be that $K_0(A)$ has non-trivial torsion, which is of course killed by the Chern character, and that would prevent $K_0(A)$ to embed into $\mathbb{R}$.