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arXiv · 2509.05524

Semigroups, groups, and algebras of dynamical origin

Volodymyr Nekrashevych
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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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Volodymyr Nekrashevych. 2025-09-05. Semigroups, groups, and algebras of dynamical origin. https://arxiv.org/abs/2509.05524

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