 

Kenneth R. Davidson and Dilian Yang
Representations of higher rank graph algebras


Published: 
May 19, 2009

Keywords: 
higher rank graph, aperiodicity condition, atomic representations, dilation 
Subject: 
47L55, 47L30, 47L75, 46L05 


Abstract
Let F_{θ}^{+} be a kgraph 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 F_{θ}^{+}
and identify a symmetry subgroup H_{θ} of Z^{k}.
If this has rank s, then C*(F_{θ}^{+}) ≅ C(T^{s}) ⊗ A
for some simple C*algebra A.


Acknowledgements
First author partially supported by an NSERC grant. Second author partially supported by the Fields Institute.


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

