Nest representations of TAF algebras.

Hopenwasser, Alan and Peters, Justin R. and Power, Stephen C. (2000) Nest representations of TAF algebras. Canadian Journal of Mathematics, 52 (6). pp. 1221-1234. ISSN 0008-414X

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.