Ideals Generated by Projections and Inductive Limit C*-algebras
by
Cornel Pasnicu
University of Puerto Rico, San Juan

We introduce two classes of inductive limit C^*-algebras which generalize the AH algebras: the GAH algebras and a subclass of it, the strong GAH algebras. Note that any AH algebra or any inductive limit of a sequence of finite direct sums of unital, simple C^*-algebras is a strong GAH algebra. Also, any inductive limit of a sequence of C^*-algebras which are finite direct sums of C^*-algebras each of which is either unital and simple or unital and projectionless is a GAH algebra. We give necessary and sufficient conditions for an ideal of a GAH algebra to be generated by projections, which, in particular, give necessary and sufficient conditions for a GAH algebra to have the ideal property (i.e. any ideal is generated by projections). We prove that if 0 --> I --> A --> B --> 0 is an exact sequence of C^*-algebras such that A is a GAH algebra then A has the ideal property if and only if I and B have the ideal property. We describe the lattice of ideals generated by projections of a strong GAH algebra and also the partially ordered set of the stably cofinite ideals generated by projections of a strong GAH algebra A under the additional assumption that the projections in M_\infty(A) satisfy the Riesz decomposition property. These results generalize some of our previous theorems involving AH algebras.

Date received: March 18, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacw-09.