Purely atomic representations of higher-rank graph C*-algebras

Abstract

We study purely atomic representations of C*-algebras associated to row-finite and source-free higher-rank graphs. We describe when purely atomic representations are unitarily equivalent and we give necessary and sufficient conditions for a purely atomic representation to be irreducible in terms of the associated projection valued measure. We also investigate the relationship between purely atomic representations, monic representations and permutative representations, and we describe when a purely atomic representation admits a decomposition consisting of permutative representations.

arXiv commentThis paper constitutes a partial replacement of arXiv:1709.00592; the latter will not be submitted for publication

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Cited by in corpus (2)

• Laplace operators in finite energy and dissipation spaces
• Irreducibility and monicity for representations of $k$-graph $C^{\ast }$-algebras