Real rank and topological dimension of higher rank graph algebras

  title={Real rank and topological dimension of higher rank graph algebras},
  author={David Pask and Adam Sierakowski and Aidan Sims},
  journal={arXiv: Operator Algebras},
We study dimension theory for the $C^*$-algebras of row-finite $k$-graphs with no sources. We establish that strong aperiodicity - the higher-rank analogue of condition (K) - for a $k$-graph is necessary and sufficient for the associated $C^*$-algebra to have topological dimension zero. We prove that a purely infinite $2$-graph algebra has real-rank zero if and only if it has topological dimension zero and satisfies a homological condition that can be characterised in terms of the adjacency… 

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