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- W2034699387 abstract "We show that, if a simple C*-algebra A is topologically finite-dimensional in a suitable sense, then not only K0(A) has certain good properties, but A is even accessible to Elliott’s classification program. More precisely, we prove the following results: If A is simple, separable and unital with finite decomposition rank and real rank zero, then K0(A) is weakly unperforated. If A has finite decomposition rank, real rank zero and the space of extremal tracial states is compact and zero-dimensional, then A has stable rank one and tracial rank zero. As a consequence, if B is another such algebra, and if A and B have isomorphic Elliott invariants and satisfy the Universal coefficients theorem, then they are isomorphic. In the case where A has finite decomposition rank and the space of extremal tracial states is compact and zero-dimensional, we also give a criterion (in terms of the ordered K0-group) for A to have real rank zero. As a byproduct, we show that there are examples of simple, stably finite and quasidiagonal C*-algebras with infinite decomposition rank." @default.
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- W2034699387 date "2005-06-14" @default.
- W2034699387 modified "2023-10-15" @default.
- W2034699387 title "On topologically finite-dimensional simple C*-algebras" @default.
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- W2034699387 doi "https://doi.org/10.1007/s00208-005-0657-z" @default.
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