48 reputation
6
bio website maths.gla.ac.uk/~gtornetta
location Glasgow, Scotland
age 26
visits member for 2 years, 10 months
seen Dec 11 '13 at 12:40
I'm working towards a Bivariant Cuntz Semigroup as a new invariant for C*-algebras.

Apr
5
comment Projective limit construction of a semigroup
Ok so the difference is just in the set $X$, and the restrictions on the universal property account for the different nature of such set $X$. Anyway that is exactly what I was expecting, for this former case actually comes from $F(C_0(\mathbb N),\mathcal K)$, where $C_0(\mathbb N)$ denotes the C*-algebra of continuous functions on $\mathcal N$ (which isn't compact) vanishing at $\infty$. So thanks a lot for your help with this matter!
Apr
5
comment Projective limit construction of a semigroup
Yes I actually meant 0 by "dropping" in this particular example. So the limit would not be a pro-ACom object, but I guess this non compact $X$ is just $\mathbb N$ in this other particular example?
Apr
5
comment Projective limit construction of a semigroup
Dear kar, thank you very much for the suggested reading and for your further explanation, it helped a lot and I think I can more clearly see the link with the Cantor set. I actually have a similar construction with $\mathbb N$ viewed as the limit of $\{1,\ldots,n\}$ with transition maps that act, on the generators, as $x_k\mapsto x_k$ for any $k=1,\ldots,n$ and $x_{n+1}$ is dropped. Hence this should lead to $\tilde{\mathbb N}^{\mathbb N}$ in the limit on the free pro-ACom semigroups.
Apr
5
comment Projective limit construction of a semigroup
I was trying to locate some references for such category of semigroups, in particular some sources about how to construct transition maps between the semigroups in the projective limit given the topological space (the Cantor set in the example in question)? Could you please refer me to some literature? That would be great. Cheers!
Apr
4
awarded  Scholar
Apr
4
comment Projective limit construction of a semigroup
The object $S$ in question arises from considering the C*-algebra C(X) of continuous functions on the Cantor set as first argument in a bivariant functor $F(C(X), \mathcal K)$, where $\mathcal K$ is the C*-algebra of compact operators. So the answer you provided makes a lot of sense in this context. Thank you very much!
Apr
4
accepted Projective limit construction of a semigroup
Apr
4
revised Projective limit construction of a semigroup
edited tags
Apr
3
asked Projective limit construction of a semigroup
Jan
13
answered *-homomorphisms between matrix algebras
Jun
28
awarded  Teacher
Mar
16
awarded  Supporter
Jul
27
awarded  Student
Jun
29
answered Is the F.T of $\operatorname{Span}(\mathscr S(\mathbb R^2)\otimes\mathscr D(D))$, $D\subset\mathbb R^2$ dense in $L^2(\mathbb R^4)$?
Jun
28
awarded  Editor
Jun
28
comment Is the F.T of $\operatorname{Span}(\mathscr S(\mathbb R^2)\otimes\mathscr D(D))$, $D\subset\mathbb R^2$ dense in $L^2(\mathbb R^4)$?
$\mathscr D(D)$ is the space of smooth function with compact support contained in a fixed bounded subset $D\subset\mathbb R^2$. Of course M. Bischoff is right, my mistake. Now I've fixed the question.
Jun
28
revised Is the F.T of $\operatorname{Span}(\mathscr S(\mathbb R^2)\otimes\mathscr D(D))$, $D\subset\mathbb R^2$ dense in $L^2(\mathbb R^4)$?
fixed error; added 1 characters in body
Jun
27
asked Is the F.T of $\operatorname{Span}(\mathscr S(\mathbb R^2)\otimes\mathscr D(D))$, $D\subset\mathbb R^2$ dense in $L^2(\mathbb R^4)$?
Jun
26
awarded  Autobiographer