Realising the Toeplitz algebra of a higher-rank graph as a Cuntz-Krieger algebra

2015/07/27 by Yosafat E. P. Pangalela, Pangalela, Yosafat E. P.
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1507.07610

openalex publication_date 2015/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a row-finite higher-rank graph Λ, we construct a higher-rank graph TΛ such that the Toeplitz algebra of Λ is isomorphic to the Cuntz-Krieger algebra of TΛ. We then prove that the higher-rank graph TΛ is always aperiodic and use this fact to give another proof of a uniqueness theorem for the Toeplitz algebras of higher-rank graphs.

Citations

• Simplicity of finitely-aligned k-graph C*-algebras
• The co-universal C*-algebra of a row-finite graph
• Adding tails to C*-correspondences

Related

• Topological higher-rank graphs and the C^*-algebras of topological 1-graphs
• Efficient Presentations of Relative Cuntz-Krieger Algebras
• Higher-rank graph algebras are iterated Cuntz-Pimsner algebras
• Higher-rank graphs and their C*-algebras
• Relative Cuntz-Krieger algebras of finitely aligned higher-rank graphs