Representations of Higher Rank Graph Algebras
by
Dilian Yang
University of Waterloo
Coauthors: Kenneth R. Davidson

We show that every irreducible atomic *-representation of a k-graph 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 a k-graph and identify a symmetry subgroup of Z^k. If this has rank s, then the graph C*-algebra is a tensor product of C(T^s) with a simple C*-algebra.

Date received: April 12, 2008