منابع مشابه
20 01 Recursive Subhomogeneous Algebras
We introduce and characterize a particularly tractable class of unital type 1 C*-algebras with bounded dimension of irreducible representations. Algebras in this class are called recursive subhomogeneous algebras, and they have an inductive description (through iterated pullbacks) which allows one to carry over from algebras of the form C(X,Mn) many of the constructions relevant in the study of...
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Let A be a unital simple direct limit of recursive subhomogeneous algebras with no dimension growth. We give criteria which specify exactly when A has real rank zero, and exactly when A has the Property (SP): every nonzero hereditary subalgebra of A contains a nonzero projection. Specifically, A has real rank zero if and only if the image of K0(A) in Aff(T (A)) is dense, and A has the Property ...
متن کاملCancellation and Stable Rank for Direct Limits of Recursive Subhomogeneous Algebras
We prove the following results for a unital simple direct limit A of recursive subhomogeneous algebras with no dimension growth: (1) tsr(A) = 1. (2) The projections in M∞(A) satisfy cancellation: if e ⊕ q ∼ f ⊕ q, then e ∼ f . (3) A satisfies Blackadar’s Second Fundamental Comparability Question: if p, q ∈ M∞(A) are projections such that τ(p) < τ(q) for all normalized traces τ on A, then p q. (...
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We show that finitely generated subhomogeneous C∗-algebras have finite decomposition rank. As a consequence, any separable ASH C∗-algebra can be written as an inductive limit of subhomogeneous C∗-algebras each of which has finite decomposition rank. It then follows from work of H. Lin and of the second named author that the class of simple unital ASH algebras which have real rank zero and absor...
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We analyze the decomposition rank (a notion of covering dimension for nuclear C-algebras introduced by E. Kirchberg and the author) of subhomogeneous C-algebras. In particular we show that a subhomogeneous C-algebra has decomposition rank n if and only if it is recursive subhomogeneous of topological dimension n and that n is determined by the primitive ideal space. As an application, we use re...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2007
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-07-03850-0