Semigroups, groups, and algebras of dynamical origin

2025/09/05 by Nekrashevych, Volodymyr · 1 citation
Physics and Astronomy · #Algebraic number #Algebraic structure #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Inverse #Inverse semigroup #Operator Algebras (math.OA) #Quantum chaos and dynamical systems #Rotation (mathematics) #Semigroup #Set (abstract data type)

paper · pdf · doi:10.48550/arxiv.2509.05524

published in arXiv (Cornell University) (Cornell University)

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.

Cited by

• Near full groups of bounded type, \rom1

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