On groupoids and \(C^*\)-algebras from self-similar actions

zbMath1479.46066arXiv2012.14519MaRDI QIDQ2045878

Valentin Deaconu

Publication date: 16 August 2021

Published in: The New York Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.14519

zbMATH Keywords

\(K\)-theoryCuntz-Pimsner algebraself-similar actionhomology of groupoidssimilarity of groupoids

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Noncommutative dynamical systems (46L55) (K)-theory and homology; cyclic homology and cohomology (19D55) General theory of (C^*)-algebras (46L05) Topological groupoids (including differentiable and Lie groupoids) (22A22) Dynamical systems and the theory of (C^*)-algebras (37A55)

Related Items (1)

The Koopman representation for self-similar groupoid actions

Cites Work

• Self-similar graphs, a unified treatment of Katsura and Nekrashevych \(C^\ast\)-algebras
• A groupoid approach to C*-algebras
• Groupoid actions on \(C^\ast\)-correspondences
• Equilibrium states on operator algebras associated to self-similar actions of groupoids on graphs
• The homology of the Katsura-Exel-Pardo groupoid
• A dichotomy for simple self-similar graph \(C^\ast \)-algebras
• Self-similar groups and their geometry
• On the \(K\)-theory of higher rank graph \(C^*\)-algebras
• Homology and topological full groups of étale groupoids on totally disconnected spaces
• Homology of odometers
• Groupoid cohomology and extensions
• C*-algebras and self-similar groups
• Generalized Cuntz-Krieger algebras
• A homology theory for étale groupoids
• HOMOLOGY AND MATUI’S HK CONJECTURE FOR GROUPOIDS ON ONE-DIMENSIONAL SOLENOIDS
• Ample groupoids: equivalence, homology, and Matui's HK conjecture

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