Noncommutative manifolds from graph and k-graph C^*-algebras

2007/01/19 by David Pask, Pask, David, Adam Rennie +3
Mathematics · Physics and Astronomy · #46L87 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.math/0701527

openalex publication_date 2007/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In previous papers, we constructed smooth (1,∞)-summable semfinite spectral triples for graph algebras with a faithful trace, and (k,∞)-summable semifinite spectral triples for k-graph algebras. In this paper we identify classes of graphs and k-graphs which satisfy a version of Connes' conditions for noncommutative manifolds.

Related

• The Noncommutative Geometry of Graph C^*-Algebras I: The Index Theorem
• Semifinite spectral triples associated with graph C*-algebras
• The Noncommutative Geometry of k-graph C*-Algebras
• Inverse Limits of Spectral Triples
• Reconstruction of manifolds in noncommutative geometry