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

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

2005-04-15

arxiv.org/abs/math/0504331v2

Mathematics

Operator Algebras

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

Scientific paper

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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