• Corpus ID: 119625506

Unbounded quasitraces, stable finiteness and pure infiniteness

@article{Pask2017UnboundedQS,
  title={Unbounded quasitraces, stable finiteness and pure infiniteness},
  author={David Pask and Adam Sierakowski and Aidan Sims},
  journal={arXiv: Operator Algebras},
  year={2017}
}

• D. Pask, Adam Sierakowski, A. Sims
• Published 3 May 2017
• Mathematics
• arXiv: Operator Algebras

We prove that if A is a \sigma-unital exact C*-algebra of real rank zero, then every state on K_0(A) is induced by a 2-quasitrace on A. This yields a generalisation of Rainone's work on pure infiniteness and stable finiteness of crossed products to the non-unital case. It also applies to k-graph algebras associated to row-finite k-graphs with no sources. We show that for any k-graph whose C*-algebra is unital and simple, either every twisted C*-algebra associated to that k-graph is stably finite, or every twisted C*-algebra associated to that k-graph is purely infinite. Finally we provide sufficient and necessary conditions for a unital simple k-graph algebra to be purely infinite in terms of the underlying k-graph.