Reputation
7,955
Top tag
Next privilege 10,000 Rep.
Access moderator tools
Badges
24 45
Newest
 Nice Answer
Impact
~198k people reached

Jan
29
comment $K$-Theory of finite dimensional Banach algebras
@Fermando: Because, for non-unital algebras $K_0(A)$ is defined as $\ker[K_0(\tilde{A})\rightarrow K_0(k)=\mathbb{Z}]$, where $\tilde{A}$ is the unitization of $A$, so you don't deal with f.g. projective modules, but with differences of modules having the same dimension.
Jan
29
comment $K$-Theory of finite dimensional Banach algebras
@Fernando: I think you are implicitly assuming that your algebra has a unit.
Jan
25
comment Spectrum of the Laplace-Beltrami operator on a domain of finite volume in the hyperbolic space $H^n$
@Vladimir: The link provided by Marcel contains a number of useful references. See also: en.wikipedia.org/wiki/Laplace–Beltrami_operator
Jan
25
comment Spectrum of the Laplace-Beltrami operator on a domain of finite volume in the hyperbolic space $H^n$
You should check Chapters XII, XIII and XIV of Serge Lang's book ``$SL_2(\mathbb{R})$'' (where SL doesn't stand for Serge Lang): you will see that, for $\Gamma=SL_2(\mathbb{Z})$, the spectrum of the Laplace operator has both a continuous and a discrete part. Everything is very explicit. On the other hand, it is a classical fact that, on a compact Riemannian manifold, the Laplace operator has compact resolvent, hence has discrete spectrum.
Jan
25
revised Construct discrete series of SL(2,R) as kernel of twisted Dirac operators
added 13 characters in body
Jan
25
answered Construct discrete series of SL(2,R) as kernel of twisted Dirac operators
Jan
24
comment Construct discrete series of SL(2,R) as kernel of twisted Dirac operators
This way you get only "half of" the discrete series of $SL_2(\mathbb{R})$, namely the holomorphic discrete series, corresponding to characters $z\mapsto z^n$ of $K$ with $n>0$. You miss the anti-holomorphic discrete series, corresponding to $n<0$.
Jan
14
comment The positive cone of the standard representation of a Von Neumann algebra
@Yemon: indeed, and weakly continuous representations as well.
Jan
8
comment Is there a link between $H_2(G,\mathbb{Z})$, the Schur Multiplier of a group, and the “other” Schur multipliers of a group?
I fully support Yemon's answer and comment! Sometimes it happens in mathematics that two completely unrelated objects have similar names...
Jan
3
comment The left regular representation of the Jacobi groups over local fields of characteristic >2 is type I?
Liminality of $H_3(K)$ ($K$ non-archimedean) follows from the explicit description of the unitary irrep's, as given e.g. in section 1.2 of V. Lafforgue's paper: vlafforg.perso.math.cnrs.fr/haagerup-rem.pdf I expect the proof to be essentially the same for $H_{2n+1}(K)$.
Dec
23
comment Which finite groups can be characterized by their automorphism groups?
Carmichael's conjecture states that the equation $\varphi(x)=n$ (where $n$ is given) never has a unique solution. This amounts to saying that the finite cyclic group $\mathbb{Z}/n\mathbb{Z}$ is never characterized by the order of its automorphism group.
Oct
24
comment Infinite k-connected planar graphs
Recently, there has been extensive work on planar Cayley graphs by Agelos Georgakopoulos, see his website: homepages.warwick.ac.uk/~maslar/pubsFrames.html
Oct
9
comment Is the sum of spectral projections a projection?
@Frank: It is rather the holomorphic functional calculus that is well-behaved... This holds in any Banach algebra!
Oct
5
comment Groups without property (T) but all finite quotients are expanders
I think Dave's example qualifies as an answer. Another example would be $SL_2(\mathbb{Z}[\sqrt{p}])$.
Sep
26
revised If all balls around fixed basepoints are isometric, are the spaces as well (length spaces)?
Fixed typos in title
Sep
26
comment Examples of a topological semidirect product
In this case $Aut(G)$ is large, as it contains e.g. the full symmetric group of the integers. And presumably you view the semi-direct product $G\rtimes Aut(G)$ as interesting (BTW, $\rtimes$ is the notation in group theory), since you prove results about it.
Sep
20
comment Examples of a topological semidirect product
OK, continuous automorphisms, then! You could look at cases where $Aut(G)$ is large, e.g. $G=C_2^\mathbb{N}$, where $C_2$ is the 2-element group.
Sep
19
comment Examples of a topological semidirect product
Automorphisms, you mean? (if you only assume homeos, the semi-direct product makes no sense...)
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