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- W2953001214 abstract "In this paper we show that certain simple locally recursive subhomogeneous (RSH) C*-algebras are tracially approximately interval algebras after tensoring with the universal UHF algebra. This involves a linear algebraic encoding of the structure of the local RSH algebra allowing us to find a path through the algebra which looks like a discrete version of [0,1] and exhausts most of the algebra. We produce an actual copy of the interval and use properties of C*-algebras tensored with UHF algebras to move the honest interval underneath the discrete version. It follows from our main result that such C*-algebras are classifiable by Elliott invariants. Our theorem requires finitely many tracial states that all induce the same state on the K_0-group; in particular we do not require that projections separate tracial states. We apply our results to classify some examples of C*-algebras constructed by Elliott to exhaust the invariant. We also give an alternate way to classify examples of Lin and Matui of C*-algebras of minimal dynamical systems. In this way our result can be viewed as a first step towards removing the requirement that projections separate tracial states in the classification theorem for C*-algebras of minimal dynamical systems given by Toms and the second named author." @default.
- W2953001214 created "2019-06-27" @default.
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- W2953001214 date "2013-07-04" @default.
- W2953001214 modified "2023-09-27" @default.
- W2953001214 title "UHF slicing and classification of nuclear C*-algebras" @default.
- W2953001214 hasPublicationYear "2013" @default.
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