Simplicity of algebras and C⁎-algebras of self-similar groupoids
Abstract
Many previously studied path algebras or self-similar group algebras may be viewed as Steinberg algebras of self-similar groupoids. By way of inverse semigroup algebras, we characterize when the Steinberg algebra of a self-similar groupoid is simple. We show that the simplicity of the reduced $C^*$-algebra of a contracting self-similar groupoid coincides with the simplicity of the Steinberg algebra. As an aside, we show that simplicity of the two algebras sometimes depends only on the skeleton of the self-similar groupoid acting on a strongly connected graph. Finally, we apply our methods to examples including a self-similar groupoid akin to multispinal self-similar groups and a self-similar groupoid built from the well-known Basilica group.
Fields of Study & Subjects
Advanced Operator Algebra Research
Advanced Algebra and Logic
Advanced Banach Space Theory
Publication details
- Journal / source
- Journal of Mathematical Analysis and Applications
- Volume
- 559
- Issue
- 1
- Pages
- 130446–130446
- Publication date
- 21 January 2026
- Language
- EN