Nest Representations of TAF Algebras

Alan Hopenwasser; Justin R. Peters; Stephen C. Power

paper

Nest Representations of TAF Algebras

arXiv:math/9905088

Abstract

A nest representation of a strongly maximal TAF algebra $A$ is a representation $π$ for which $Lat π (A) i s t o t a l l y or d er e d . W e p r o v e t ha t i f t h es p ec t r u m o f$ A $i s t o t a l l y or d er e d, or i f$ \operatorname{Lat} π(A) $co n t ain s ana t o m, t h e n$ \operatorname{ker} π$ is a meet irreducible ideal.

AMS-LaTeX, 17 pages. Revised version corrects a misstatement in the expository material of the main theorem in section 3. Other minor misprints are also corrrected