Meet irreducible ideals in direct limit algebras

TL;DR

This paper investigates meet irreducible ideals in certain direct limit algebras, extending known descriptions from upper triangular matrices to more complex algebraic structures, with additional insights under specific conditions.

Contribution

It provides a new description of meet irreducible ideals in strongly maximal triangular subalgebras of AF C*-algebras, including cases with analytic subalgebras and injective 0-cocycles.

Findings

Description of meet irreducible ideals in terms of spectrum

Extension of ideal descriptions from matrices to limit algebras

A distance formula for completely meet irreducible ideals

Abstract

We study the meet irreducible ideals in certain direct limit algebras, namely the strongly maximal triangular subalgebras of AF C*-algebras. These ideals have a description in terms of the coordinates, or spectrum, that is a natural extension of one description of meet irreducible ideals in the upper triangular matrices. Additional information is available if the limit algebra is an analytic subalgebra of its C*-envelope or if the analytic algebra is trivially analytic with an injective 0-cocycle. Completely meet irreducible ideals are considered, and a distance formula is presented.