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Abstract: Let $\Fth$ be a $\Bk$-graph on a single vertex. We show that everyirreducible atomic $*$-representation is the minimal $*$-dilation of a groupconstruction representation. It follows that every atomic representationdecomposes as a direct sum or integral of such representations. We characterizeperiodicity of $\Fth$ and identify a symmetry subgroup $H \theta$ of $\bZ^\Bk$.If this has rank $s$, then $\ca\Fth \cong C\bT^s \otimes \fA$ for somesimple C*-algebra $\fA$.



Author: Kenneth R. Davidson, Dilian Yang

Source: https://arxiv.org/







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