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Results tagged with c-star-algebras
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user 1291
A C*-algebra is a complex Banach algebra together with an isometric antilinear involution satisfying (a b)* = b* a* and the C*-identity ‖a* a‖ = ‖a‖². Related tags: [banach-algebras], [von-neumann-algebras], [operator-algebras], [spectral-theory].
5
votes
When is a groupoid the path groupoid of a graph?
This is an answer to the question: "Given a $C^\ast$-algebra $A$ that shares some properties of (higher-rank) graph algebras (such as separability, nuclearity, UCT, K-theoretic properties), can I conc …
- 3,174
2
votes
Relative K-theory and split exact sequences of C* algebras
The unitalization case $A=J^+$ is treated in Blackadar's $K$-theory for Operator Algebras. In Proposition 5.4.1 he directly shows that
$$
K_0(J^+,J)\cong\ker(K_0(J^+)\to K_0({J^+}/J)).
$$
- 3,174
4
votes
0
answers
454
views
What is the spectrum of the commutative C*-algebra I have constructed here?
Let $B$ and $F$ be compact Hausdorff spaces.
Let $E\to B$ be a fiber bundle with fibre $F$ and structure group $\mathrm{Homeo}(F)$, the group of homeomorphisms of $F$.
I think this induces a fiber b …
- 3,174
13
votes
1
answer
1k
views
What is the commutative analogue of a C*-subalgebra?
Using the duality between locally compact Hausdorff spaces and commutative $C^*$-algebras one can write down a vocabulary list translating topological notions regarding a locally compact Hausdorff spa …
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0
votes
Accepted
Relation between the UCT and Künneth ($C^*$-algebras)
It is absolutely true that these two theorems are conceptually related. But instead of one being a consequence of the other, both rather follow from the same machinery being applied to slightly differ …
- 3,174
2
votes
Gelfand duality in NCG
Concerning your last question, I would say you should view your C*-algebra itself as the (coordinate ring on the) "non-commutative topological space." The spaces you suggest are commutative. Your C*-a …
- 3,174
9
votes
2
answers
2k
views
What does the representation theory of the reduced C*-algebra correspond to?
Let $G$ be a locally compact group. The group C*-algebra $C^* (G)$ is designed to come with a natural bijection between its (nondegenerate) representations and the (strongly continuous, unitary) repre …
- 3,174
9
votes
$C^{*}$-correspondences viewed as generalized endomorphisms
Expanding my comment as per suggestion above. All this is explained in more detail in the reference I gave though.
A correspondence from $A$ to $B$ is a Hilbert $B$-module on which $A$ acts non-degen …
- 3,174
1
vote
Accepted
Unitization via "End points compactification"
There is Noncommutative End Theory by Akemann and Eilers.
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6
votes
1
answer
870
views
Sources for exact triangles in triangulated categories.
The other day I came across the statement that in the triangulated category $\mathfrak{KK}$ (of C*-algebras with KK-groups as morphism sets) "there are many other sources of exact triangles besides ex …
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