Skip to main content
placeholder image

Unbounded quasitraces, stable finiteness and pure infiniteness

Journal Article


Abstract


  • We prove that if A is a σ-unital exact C∗-algebra of real rank zero, then every state on K0(A) extends to 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 a twisted C∗-algebra of a cofinal k-graph with no sources, stable finiteness is independent of the twisting cocycle. We also study pure infiniteness of twisted higher rank graph C∗-algebras.

Publication Date


  • 2019

Citation


  • Pask, D., Sierakowski, A., & Sims, A. (2019). Unbounded quasitraces, stable finiteness and pure infiniteness. Houston Journal of Mathematics, 45(3), 763-814.

Scopus Eid


  • 2-s2.0-85082648095

Web Of Science Accession Number


Start Page


  • 763

End Page


  • 814

Volume


  • 45

Issue


  • 3

Abstract


  • We prove that if A is a σ-unital exact C∗-algebra of real rank zero, then every state on K0(A) extends to 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 a twisted C∗-algebra of a cofinal k-graph with no sources, stable finiteness is independent of the twisting cocycle. We also study pure infiniteness of twisted higher rank graph C∗-algebras.

Publication Date


  • 2019

Citation


  • Pask, D., Sierakowski, A., & Sims, A. (2019). Unbounded quasitraces, stable finiteness and pure infiniteness. Houston Journal of Mathematics, 45(3), 763-814.

Scopus Eid


  • 2-s2.0-85082648095

Web Of Science Accession Number


Start Page


  • 763

End Page


  • 814

Volume


  • 45

Issue


  • 3