Phoenix87
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Registered User
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I'm working towards a Bivariant Cuntz Semigroup as a new invariant for C*-algebras.
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Apr 5 |
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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! |
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Apr 5 |
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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? |
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Apr 5 |
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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. |
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Apr 5 |
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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! |
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Apr 4 |
awarded | ● Scholar |
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Apr 4 |
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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! |
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Apr 4 |
revised |
Projective limit construction of a semigroup edited tags |
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Apr 3 |
asked | Projective limit construction of a semigroup |
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Jan 13 |
answered | *-homomorphisms between matrix algebras |
