The topology of ideals in some triangular AF algebras

TL;DR

This paper characterizes the topology of ideals in certain triangular AF algebras, establishing a correspondence between closed sets of ideals and the algebra's structure, with links to nest representations.

Contribution

It introduces a topological framework for the set of meet-irreducible ideals in maximal triangular AF algebras, connecting ideal topology with algebraic and representation-theoretic properties.

Findings

Meet-irreducible ideals form a topological space under hull-kernel closure.

There is a one-to-one correspondence between closed sets of ideals and the algebra.

Connections with nest representations and nest-primitive ideals are established.

Abstract

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.