The Spectral Theorem for Bimodules in Higher Rank Graph C*-algebras
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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- April 2005
- DOI:
- 10.48550/arXiv.math/0504331
- arXiv:
- arXiv:math/0504331
- Bibcode:
- 2005math......4331H
- Keywords:
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- Mathematics - Operator Algebras;
- 47L40
- E-Print:
- Minor typographical errors corrected. Paper will appear in the Illinois Journal of Mathematics