Noncommutative manifolds from graph and k-graph c*-algebras

David Pask; Adam Rennie; Aidan Sims

doi:10.1007/s00220-009-0926-x

Noncommutative manifolds from graph and k-graph c*-algebras

David Pask, Adam Rennie^*, Aidan Sims

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

In [PRen] we constructed smooth (1, ∞)-summable semifinite spectral triples for graph algebras with a faithful trace, and in [PRS] we constructed (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.

Original language	English
Pages (from-to)	607-636
Number of pages	30
Journal	Communications in Mathematical Physics
Volume	292
Issue number	3
DOIs	https://doi.org/10.1007/s00220-009-0926-x
Publication status	Published - Oct 2009

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title = "Noncommutative manifolds from graph and k-graph c*-algebras",

abstract = "In [PRen] we constructed smooth (1, ∞)-summable semifinite spectral triples for graph algebras with a faithful trace, and in [PRS] we constructed (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.",

author = "David Pask and Adam Rennie and Aidan Sims",

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AU - Rennie, Adam

AU - Sims, Aidan

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AB - In [PRen] we constructed smooth (1, ∞)-summable semifinite spectral triples for graph algebras with a faithful trace, and in [PRS] we constructed (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.

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DO - 10.1007/s00220-009-0926-x

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VL - 292

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EP - 636

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 3

ER -

Noncommutative manifolds from graph and k-graph c*-algebras

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