KMS weights on groupoid and graph C*-algebras

2013/06/21 by Klaus Thomsen, Thomsen, Klaus
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.1306.5118

26 pages, 2 figures

arxiv created 2013/06/21 · openalex publication_date 2013/06/21 · arxiv updated 2013/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper contains a description of the KMS weights for the one-parameter action on the reduced C*-algebra of a second countable locally compact Hausdorff etale groupoid, arising from a continuous real valued homomorphism satisfying two conditions. The results are subsequently applied to identify the KMS weights for the gauge action on a simple graph algebra. The von Neumann algebra generated by the GNS-representation of an extremal KMS weight is a factor, and tools are developed to determine its type. The paper concludes with three examples to illustrate the results.

Citations

• KMS-weights on C*-algebras
• Weight theory for C*-algebraic quantum groups

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• KMS weights on graph C*-algebras II Factor types and ground states
• The factor type of conservative KMS weights on graph C*-algebras
• Diagonality of actions and KMS weights
• The structure of KMS weights on étale groupoid C^*-algebras