New York Journal of Mathematics
Volume 15 (2009) 169-198


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

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.


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

Dilian Yang:
Mathematics and Statistics Department, University of Windsor, Windsor, ON N9B 3P4 CANADA