Simplicity of C*-Algebras of Contracting Self-Similar Groups
Journal article, 2025
We show that the C∗-algebra associated by Nekrashevych to a contracting self-similar group is simple if and only if the corresponding complex ∗-algebra is simple. We also improve on Steinberg and Szakács’s algorithm to determine if the ∗-algebra is simple. This provides an interesting class of non-Hausdorff, amenable, effective and minimal ample groupoids for which simplicity of the C∗-algebra and the complex ∗-algebra are equivalent.
Author
Eusebio Gardella
University of Gothenburg
Chalmers, Mathematical Sciences, Analysis and Probability Theory
Volodymyr Nekrashevych
Texas A&M University
Benjamin Steinberg
City University of New York (CUNY)
Alina Vdovina
City University of New York (CUNY)
Communications in Mathematical Physics
0010-3616 (ISSN) 1432-0916 (eISSN)
Vol. 406 10 251Subject Categories (SSIF 2025)
Algebra and Logic
DOI
10.1007/s00220-025-05411-5