October 12, 2025Open Access

Semigroups, groups, and algebras of dynamical origin

Key Points

Algebraic structures such as semigroups and groupoids provide insights into partial symmetries and their applications.
The study details the definitions and constructions of contracting self-similar inverse semigroups, enhancing our theoretical framework.
Examples like the semigroup from the golden mean rotation illustrate real-world applications of these abstract concepts.
Topics include Steinberg algebras and C*-algebras, which further bridge connections between algebra and dynamical systems.

Abstract

The paper is an overview of recent results on algebraic structures (semigroups, groupoids, algebras, inverse semigroups, and groups) associated with objects with a rich set of partial symmetries. We discuss etale groupoids and inverse semigroups, Steinberg algebras, C*-algebras, topological full groups etc.. In particular, we describe in detail the main definitions and constructions related to contracting self-similar inverse semigroups. They are illustrated by several examples, including the semigroup generated by the golden mean rotation and the tiling semigroup of the Penrose tiling.

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Cite This Study

Volodymyr Nekrashevych (Fri,) studied this question.

synapsesocial.com/papers/68ec384042a190b2c35198be https://doi.org/https://doi.org/10.48550/arxiv.2509.05524