Representations of Higher Rank Graph Algebras

Abstract

Let $\Fth$ be a $\Bk$-graph on a single vertex. We show that every irreducible atomic $\ast$-representation is the minimal $\ast$-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 $\Fth$ and identify a symmetry subgroup $H_{\theta }$ of $\bZ^\Bk$. If this has rank $s$, then $\ca(\Fth) \cong \rC(\bT^s) \otimes \fA$ for some simple C*-algebra $\fA$.

30 pages

References in corpus (4)

• Higher rank graph C*-algebras
• Periodicity in Rank 2 Graph Algebras
• Classifying Higher Rank Analytic Toeplitz Algebras
• Poisson transform for higher-rank graph algebras and its applications

Cited by in corpus (8)

• Finitely Correlated Representations of Product Systems of $C^{\ast }$-Correspondences over ${\mathbb{N}}^k$
• Periodic higher rank graphs revisited
• Nonself-adjoint 2-graph algebras
• Purely atomic representations of higher-rank graph C*-algebras
• Graphs of $C^{\ast }$-correspondences and Fell bundles
• Separable representations of higher-rank graphs
• Cycline subalgebras of $k$-graph C*-algebras
• C^*-algebras from k group representations