2021/12/29 by Valentin Deaconu, Deaconu, Valentin
Mathematics · Medicine · Physics and Astronomy · #46L05 #Advanced Neuroimaging Techniques and Applications #Advanced Operator Algebra Research #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2112.14341
openalex publication_date 2021/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the C^*-algebra C^*(κ) generated by the Koopman representation κ of an étale groupoid G acting on a measure space (X,μ). We prove that for a level transitive self-similar action (G,E) with E finite and |uE1| constant, there is an invariant measure ν on X=E^∞ and that C^*(κ) is residually finite-dimensional with a normalized self-similar trace. We also discus p-fold similarities of Hilbert spaces in connection to representations of the graph algebra C^*(E) and self-similar representations of G in connection to the Cuntz-Pimsner algebra C^*(G,E).