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

Alan Hopenwasser
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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.

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Alan Hopenwasser. 2005-05-30. The Spectral Theorem for Bimodules in Higher Rank Graph C*-algebras. https://arxiv.org/abs/math/0504331

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