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Nest Representations of TAF Algebras

Published online by Cambridge University Press:  20 November 2018

Alan Hopenwasser ,
Justin R. Peters  and
Stephen C. Power
Alan Hopenwasser
Affiliation:
Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487, USA email: ahopenwa@euler.math.ua.edu
Justin R. Peters
Affiliation:
Department of Mathematics, Iowa State University, Ames, IA, USA email: peters@iastate.edu
Stephen C. Power
Affiliation:
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK email: s.power@lancaster.ac.uk
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Abstract

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A nest representation of a strongly maximal $\text{TAF}$ algebra $A$ with diagonal $D$ is a representation $\pi $ for which $\text{Lat}\,\pi \left( A \right)$ 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 $\text{ }\!\!\pi\!\!\text{ }{{\left( D \right)}^{\prime \prime }}$ contains an atom.

Keywords

47L4047L35nest representationmeet irreducible idealstrongly maximal TAF algebra
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 52 , Issue 6 , 01 December 2000 , pp. 1221 - 1234
Copyright
Copyright © Canadian Mathematical Society 2000

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