The Spectral Theorem for Bimodules in Higher Rank Graph C*-algebras

2005/04/15 by Alan Hopenwasser, Hopenwasser, Alan · 1 citation
Mathematics · #47L40 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:47L40

paper · pdf · doi:10.48550/arxiv.math/0504331

Minor typographical errors corrected. Paper will appear in the Illinois Journal of Mathematics

arxiv created 2005/05/30 · arxiv updated 2009/12/01

Abstract

In this note we extend the spectral theorem for bimodules to the higher rank graph C*-algebra context. Under the assumption that the graph is row finite and has no sources, we show that a bimodule over a natural abelian subalgebra is determined by its spectrum iff it is generated by the Cuntz-Krieger partial isometries which it contains iff the bimodule is invariant under the gauge automorphisms. We also show that the natural abelian subalgebra is a masa iff the higher rank graph satisfies an aperiodicity condition.

Cited by

• On Diagonal bimodules of étale groupoid C^*-algebras

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