Journal of Operator Theory

Volume 37, Issue 1, Winter 1997 pp. 91-109.

The topology of ideals in some triangular AF algebras

Authors: Michael P. Lamoureux
Author institution:Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N.W., Calgary, AB T2N 1N4, CANADA

Summary: A set of meet-irreducible ideals is described for a class of maximal triangular almost finite algebras. This set forms a topological space under the hull-kernel closure, and there is a one-to-one correspondence between closed sets in this space and ideals in the AF algebra. Some connections with nest representations and nest-primitive ideals are also described.

Keywords: Almost finite algebra, lattice of ideals, meet-irreducible, nests of subspaces.

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