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Yemon Choi
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Reference for structure of subhomogeneussubhomogeneous C*-algebras?

Recall that a C*-algebra is subhomogeneussubhomogeneous if there is some $n$ such that the dimension of $H$ is at most $n$ for every irreducible representation $\pi \colon A \to \mathcal{B}(H)$ on some Hilbert space $H$.

For instance, abelian C*-algebras are subhomogeneussubhomogeneous (just take $n=1$).

Question: is there a reference for the structure of a subhomogeneussubhomogeneous C*-algebra?

By 'structure' I'm thinking about some explicit description, such as

$A \cong p_0 (C_0(X_0) \otimes M_{m_0}) p_0 \oplus \dots \oplus p_n (C_0(X_n) \otimes M_{m_n}) p_n$

for some locally compact Hausdorff spaces $X_0, \dots, X_n$, some $m_0, \dots, m_n \in \mathbb{N}$ and some projections $p_i \in C_0(X_i) \otimes M_{n_i}$. In my mind each $X_i$ would be the closed component of the primitive ideal of $A$ corresponding to representations of dimension $i$, for instance.

Reference for structure of subhomogeneus C*-algebras?

Recall that a C*-algebra is subhomogeneus if there is some $n$ such that the dimension of $H$ is at most $n$ for every irreducible representation $\pi \colon A \to \mathcal{B}(H)$ on some Hilbert space $H$.

For instance, abelian C*-algebras are subhomogeneus (just take $n=1$).

Question: is there a reference for the structure of a subhomogeneus C*-algebra?

By 'structure' I'm thinking about some explicit description, such as

$A \cong p_0 (C_0(X_0) \otimes M_{m_0}) p_0 \oplus \dots \oplus p_n (C_0(X_n) \otimes M_{m_n}) p_n$

for some locally compact Hausdorff spaces $X_0, \dots, X_n$, some $m_0, \dots, m_n \in \mathbb{N}$ and some projections $p_i \in C_0(X_i) \otimes M_{n_i}$. In my mind each $X_i$ would be the closed component of the primitive ideal of $A$ corresponding to representations of dimension $i$, for instance.

Reference for structure of subhomogeneous C*-algebras?

Recall that a C*-algebra is subhomogeneous if there is some $n$ such that the dimension of $H$ is at most $n$ for every irreducible representation $\pi \colon A \to \mathcal{B}(H)$ on some Hilbert space $H$.

For instance, abelian C*-algebras are subhomogeneous (just take $n=1$).

Question: is there a reference for the structure of a subhomogeneous C*-algebra?

By 'structure' I'm thinking about some explicit description, such as

$A \cong p_0 (C_0(X_0) \otimes M_{m_0}) p_0 \oplus \dots \oplus p_n (C_0(X_n) \otimes M_{m_n}) p_n$

for some locally compact Hausdorff spaces $X_0, \dots, X_n$, some $m_0, \dots, m_n \in \mathbb{N}$ and some projections $p_i \in C_0(X_i) \otimes M_{n_i}$. In my mind each $X_i$ would be the closed component of the primitive ideal of $A$ corresponding to representations of dimension $i$, for instance.

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Reference for structure of subhomogeneus C*-algebras?

Recall that a C*-algebra is subhomogeneus if there is some $n$ such that the dimension of $H$ is at most $n$ for every irreducible representation $\pi \colon A \to \mathcal{B}(H)$ on some Hilbert space $H$.

For instance, abelian C*-algebras are subhomogeneus (just take $n=1$).

Question: is there a reference for the structure of a subhomogeneus C*-algebra?

By 'structure' I'm thinking about some explicit description, such as

$A \cong p_0 (C_0(X_0) \otimes M_{m_0}) p_0 \oplus \dots \oplus p_n (C_0(X_n) \otimes M_{m_n}) p_n$

for some locally compact Hausdorff spaces $X_0, \dots, X_n$, some $m_0, \dots, m_n \in \mathbb{N}$ and some projections $p_i \in C_0(X_i) \otimes M_{n_i}$. In my mind each $X_i$ would be the closed component of the primitive ideal of $A$ corresponding to representations of dimension $i$, for instance.