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## Nest representations of TAF algebras.

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Journal publication date 2000 Canadian Journal of Mathematics 6 52 14 1221-1234 Published English

### 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.