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# Reduction to Dimension Two of Local Spectrum for $AH$ Algebra with Ideal Property

Published:2017-04-13
Printed: Dec 2017
• Chunlan Jiang,
Hebei Normal University, Shijiazhuang, China
 Format: LaTeX MathJax PDF

## Abstract

A $C^{*}$-algebra $A$ has the ideal property if any ideal $I$ of $A$ is generated as a closed two sided ideal by the projections inside the ideal. Suppose that the limit $C^{*}$-algebra $A$ of inductive limit of direct sums of matrix algebras over spaces with uniformly bounded dimension has ideal property. In this paper we will prove that $A$ can be written as an inductive limit of certain very special subhomogeneous algebras, namely, direct sum of dimension drop interval algebras and matrix algebras over 2-dimensional spaces with torsion $H^{2}$ groups.
 Keywords: AH algebra, reduction, local spectrum, ideal property
 MSC Classifications: 46L35 - Classifications of $C^*$-algebras

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