Factoriality and type classification of \textsf{k}-graph von Neumann algebras

Abstract

Let $\Fth$ be a single vertex \textsf{k}-graph, and ${\pi }_{\omega }({Ø}_{\theta })"$ be the von Neumann algebra induced from the GNS representation of a distinguished state $\omega$ of its $\text{k}$-graph C*-algebra ${Ø}_{\theta }$. In this paper, we prove the factoriality of ${\pi }_{\omega }({Ø}_{\theta })"$ and further determine its type, when either $\Fth$ has the little pull-back property, or the intrinsic group of $\Fth$ has rank $0$. The key step to achieve this is to show that the fixed point algebra of the modular action corresponding to $\omega$ has a unique tracial state.

23 pages, to appear in Proceedings of the Edinburgh Mathematical Society

References in corpus (2)

• Simplicity of C*-algebras associated to higher-rank graphs
• Nonself-adjoint 2-graph algebras

Cited by in corpus (2)

• von Neuman algebras of strongly connected higher-rank graphs
• KMS states on the C*-algebra of a higher-rank graph and periodicity in the path space