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# Nest Representations of TAF Algebras

Published:2000-12-01
Printed: Dec 2000
• Alan Hopenwasser
• Justin R. Peters
• Stephen C. Power
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## Abstract

A nest representation of a strongly maximal TAF algebra $A$ with diagonal $D$ is a representation $\pi$ for which $\lat \pi(A)$ is totally ordered. We prove that $\ker \pi$ is a meet irreducible ideal if the spectrum of $A$ is totally ordered or if (after an appropriate similarity) the von Neumann algebra $\pi(D)''$ contains an atom.
 Keywords: nest representation, meet irreducible ideal, strongly maximal TAF algebra
 MSC Classifications: 47L40 - Limit algebras, subalgebras of $C^*$-algebras 47L35 - Nest algebras, CSL algebras