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Kenneth R. Davidson and Dilian Yang
Representations of higher rank graph algebras
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| Published: |
May 19, 2009
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| Keywords: |
higher rank graph, aperiodicity condition, atomic representations, dilation |
| Subject: |
47L55, 47L30, 47L75, 46L05 |
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Abstract
Let Fθ+ be a k-graph on a single vertex.
We show that every irreducible atomic *-representation is the
minimal *-dilation of a group construction representation.
It follows that every atomic representation decomposes as a direct sum or
integral
of such representations. We characterize periodicity of Fθ+
and identify a symmetry subgroup Hθ of Zk.
If this has rank s, then C*(Fθ+) ≅ C(Ts) ⊗ A
for some simple C*-algebra A.
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| Acknowledgements
First author partially supported by an NSERC grant. Second author partially supported by the Fields Institute.
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| Author information
Kenneth R. Davidson:
Pure Math. Dept., University of Waterloo, Waterloo, ON N2L 3G1, CANADA
krdavids@uwaterloo.ca
Dilian Yang:
Mathematics and Statistics Department, University of Windsor, Windsor, ON N9B 3P4 CANADA
dyang@uwindsor.ca
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