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

2016/07/26 by Chunlan Jiang, Jiang, Chunlan
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA

paper · pdf · doi:10.48550/arxiv.1607.07578

21 pages. arXiv admin note: text overlap with arXiv:1607.07575 Accept by Canadian Mathematical Bulletin

arxiv created 2017/04/22 · arxiv updated 2017/04/25

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 H² groups.

Citations

• A Reduction theorem for AH algebras with ideal property

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