New York Journal of Mathematics
Volume 27 (2021), 923-942


Valentin Deaconu

On groupoids and C*-algebras from self-similar actions

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Published: July 6, 2021.
Keywords: Homology of groupoids; self-similar action; similarity of groupoids; Cuntz-Pimsner algebra; K-theory.
Subject: Primary 46L05.

Given a self-similar groupoid action (G,E) on the path space of a finite graph, we study the associated Exel-Pardo étale groupoid g(G,E) and its C*-algebra
C*(G,E). We review some facts about groupoid actions, skew products and semi-direct products and generalize a result of Renault about similarity of groupoids which resembles Takai duality. We also describe a general strategy to compute the K-theory of C*(G,E) and the homology of g(G,E) in certain cases and illustrate with an example.



Author information

Valentin Deaconu:
Department of Mathematics & Statistics
University of Nevada
Reno, NV 89557-0084, USA