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Reduction to Dimension Two of the Local Spectrum for an AH Algebra with the Ideal Property

Published online by Cambridge University Press:  20 November 2018

Chunlan Jiang
Chunlan Jiang*
Affiliation:
Department of Mathematics, Hebei Normal University, Shijiazhuang, China e-mail: cljiang@hebtu.edu.cn
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Abstract

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A ${{C}^{*}}$-algebra Ahas 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 the 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

46L35AH algebrareductionlocal spectrumideal property
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 4 , 01 December 2017 , pp. 791 - 806
Copyright
Copyright © Canadian Mathematical Society 2017

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