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

Jiang, Chunlan

Canadian mathematical bulletin, Tome 60 (2017) no. 4, pp. 791-806

Résumé

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.

Détail

DOI : 10.4153/CMB-2016-100-3

Mots-clés : 46L35, AH algebra, reduction, local spectrum, ideal property

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