All Questions
Tagged with limits-and-colimits c-star-algebras
7 questions
5
votes
1
answer
245
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Colimits of short exact sequences of C*-algebras
Assume I have an inductive system of short exact sequences of $C^{\ast}$-algebras (i.e., short exact sequences $0 \to A_n \to B_n \to C_n \to 0$ together with transformations from the $n$-th to the $(...
- 2,998
5
votes
0
answers
221
views
Pushout of $C^*$-algebras using generalised morphisms
There is a known construction of pushout of $C^*$-algebras, or rather, the amalgamated free product, which is universal for commutative squares of $*$-homomorphisms. Jensen and Thomsen in their book ...
- 35.5k
2
votes
0
answers
116
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Primitive ideals of inductive limits of $C^*$-algebras
I am trying to understand ideals of direct limits in the category of $C^{\ast}$-algebras.
Let $(A_n,f_n)$ be a direct sequence of $C^{\ast}$-algebras and let $I$ be a primitive (modular) ideal of ...
- 1,115
5
votes
1
answer
279
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Behaviour of direct limit with matrices
I am trying to understand direct limits in the category of $C^*$-algebras by self reading. My last question was also related to direct limits. Here is another of my doubts:
Let $(A_n,f_n)$ be a ...
- 1,115
7
votes
0
answers
555
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maximal tensor product commutes with inductive limits
Let $(A_n, \phi_n)$ be an inductive system of $C^*$ algebras and let $B$ be an arbitary $C^*$ algebra.
I want to prove $(\varinjlim A_n)\otimes_{max} B \cong \varinjlim (A_n \otimes_{max} B)$. This ...
- 1,188
14
votes
1
answer
616
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How "nondegenerate" are amalgamated free products of C*-algebras?
In the following, I assume all algebras are unital. Let $A$ and $B$ be C*-algebras that each contain (isomorphic copies of) a common C*-subalgebra $C$. Let $A *_C B$ denote the amalgamated free ...
- 5,407
11
votes
1
answer
1k
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Do direct limits (filtered colimits) commute with pullbacks, in C*-algebras?
I asked this question already on math.stackexchange, but maybe it is also useful to ask this here, since it was not answered there.
Suppose we have three directed sequences of $C^*$-algebras, say $(...
- 113