Reduction to dimension two of local spectrum for $AH$ algebra with ideal property

Chunlan Jiang

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arXiv · 1607.07578

Reduction to dimension two of local spectrum for $AH$ algebra with ideal property

Chunlan Jiang

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Abstract

A $C^{*}$-algebra $A$ has 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.

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Chunlan Jiang. 2016-07-26. Reduction to dimension two of local spectrum for $AH$ algebra with ideal property. https://arxiv.org/abs/1607.07578

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