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Extensions by C*-algebras of real rank zero,III

Published online by Cambridge University Press:  01 May 1998

H Lin
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Abstract

We give a complete classification (up to unitary equivalence) of extensions of $C(X)$ by a separable simple AF-algebra $A$ with a unique trace (up to scalar multiples), where $X$ is a compact subset of the plane. In particular, we show that there are non-trivial extensions $\tau$ such that $[\tau]=0$ in ${\rm Ext}(C(X),A).$ A new index is introduced to determine when an extension is trivial. Extensions of $C(S^2)$ and other algebras are also studied. Our results work for a larger class of C*-algebras of real rank zero.

1991 Mathematics Subject Classification: primary 46L05,46L35; secondary 46L80.

Keywords

C*-algebra extensionsreal rank zero$K$-theory
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 76 , Issue 3 , May 1998 , pp. 634 - 666
Copyright
London Mathematical Society 1998

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