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

Abstract

A $C^{\ast }$-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 $C^{\ast }$-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.

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

References in corpus (2)

• A classification of inductive limit $C^{\ast }$-algebras with ideal property
• A Reduction theorem for $AH$ algebras with ideal property

Cited by in corpus (1)

• A classification of inductive limit $C^{\ast }$-algebras with ideal property