bio | website | www2.unine.ch/alain.valette |
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location | Neuchâtel, Switzerland | |
age | 56 | |
visits | member for | 4 years, 4 months |
seen | 16 mins ago | |
stats | profile views | 5,038 |
Jul
8 |
comment |
Exotic group topologies on the affine group $ax+b$
Have you noticed that $K$ is isomorphic (as a group) to the additive group of the real line? Can you put a compact group topology on $\mathbb{R}$? |
Jul
5 |
comment |
Which journals publish research announcements?
CRAS academie-sciences.fr/activite/cr.htm |
Jun
6 |
awarded | Nice Answer |
May
27 |
comment |
How does the solenoid structure of $\mathbb{A}/\mathbb{Q}$ lift to $PGL(2, \mathbb{A})/ PGL(2, \mathbb{Q})$?
An easier question, which I think must be answered first, is: what is $\mathbb{Q}\backslash\mathbb{A}$? For answers, see e.g. this paper by A. Robert: retro.seals.ch/… You may also enjoy Weil's Basic number theory. |
May
16 |
comment |
Which p-adic algebraic groups are type I?
Thanks to David for reviving my question of 2 years ago. My reason for asking was a computation (joint with Henrik Petersen) of $L^2$-Betti numbers for locally compact groups, valid under a type I assumption; see arxiv.org/pdf/1307.0379.pdf |
May
16 |
revised |
Which p-adic algebraic groups are type I?
corrected spelling |
May
16 |
comment |
Which p-adic algebraic groups are type I?
Thanks David, welcome to MO! |
May
12 |
awarded | Nice Answer |
May
3 |
comment |
Describe the desired features of a “Mathematics Colloquium”?
My advice for colloquium speakers, is to target 1st year graduate students in the audience. |
Apr
27 |
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How does one calculate/estimate/guarantee the girth of a non-Abelian Cayley graph?
Probably not, as the word "girth" does not appear in that paper... |
Apr
27 |
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How generic are Cayley graphs of non-Abelian groups with logarithmic girth?
@Anirbit: If $G$ is abelian non-cyclic, than the girth is at most 4 because $[a,b]=aba^{-1}b^{-1}=1$ for every $a,b\in G$. If $G$ is metabelian, i.e. solvable of degree 2, then the girth is at most 16 because $[[a,b],[c,d]]=1$ for every $a,b,c,d\in G$. Etc... |
Apr
27 |
answered | How does one calculate/estimate/guarantee the girth of a non-Abelian Cayley graph? |
Apr
26 |
comment |
How generic are Cayley graphs of non-Abelian groups with logarithmic girth?
@user6818: If $G$ is solvable of solvability degree $n$, then the girth of any Cayley graph is at most $4^n$ (= the length of an $n$-iterated commutator in the generators of a free group). So you may forget about solvable groups. |
Apr
26 |
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How generic are Cayley graphs of non-Abelian groups with logarithmic girth?
math1.math.huji.ac.il/~alexlub/PAPERS/ramanujan%20graphs/… |
Apr
26 |
comment |
How generic are Cayley graphs of non-Abelian groups with logarithmic girth?
@Anirbit: Theorem 3.4 in LPS is exactly the logarithmic girth!!! |
Apr
26 |
comment |
How generic are Cayley graphs of non-Abelian groups with logarithmic girth?
@Anirbit: The Ramanujan graphs based on $SL_2(\mathbb{F}_p)$ have logarithmic girth, see the 1988 by A. Lubotzky, R. Phillips and P. Sarnak in Combinatorica. |
Apr
26 |
awarded | rt.representation-theory |
Apr
25 |
answered | Irreducible representation of $C^*(D_\infty)$, group $C^*$-algebra of an infinite dihedral group |
Apr
25 |
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 |
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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 |