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Autori principali: Margolis, Stuart, Rhodes, John
Natura: Preprint
Pubblicazione: 2024
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Accesso online:https://arxiv.org/abs/2410.06668
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author Margolis, Stuart
Rhodes, John
author_facet Margolis, Stuart
Rhodes, John
contents The theory of flows was used as a crucial tool in the recent proof by Margolis, Rhodes and Schilling that Krohn-Rhodes complexity is decidable. In this paper we begin a systematic study of aperiodic flows. We give the foundations of the theory of flows and give a unified approach to the Presentation Lemma and its relations to flows and the Slice Theorem. We completely describe semigroups having a flow over the trivial semigroup and connect this to classical results in inverse semigroup theory. We reinterpret Tilson's Theorem on the complexity of small monoids in terms of flows. We conclude with examples of semigroups built from the character table of Abelian Groups that have an aperiodic flows.
format Preprint
id arxiv_https___arxiv_org_abs_2410_06668
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Aperiodic Flows on Finite Semigroups: Foundations and First Examples
Margolis, Stuart
Rhodes, John
Dynamical Systems
Group Theory
20M20, 20M35, 20M18
The theory of flows was used as a crucial tool in the recent proof by Margolis, Rhodes and Schilling that Krohn-Rhodes complexity is decidable. In this paper we begin a systematic study of aperiodic flows. We give the foundations of the theory of flows and give a unified approach to the Presentation Lemma and its relations to flows and the Slice Theorem. We completely describe semigroups having a flow over the trivial semigroup and connect this to classical results in inverse semigroup theory. We reinterpret Tilson's Theorem on the complexity of small monoids in terms of flows. We conclude with examples of semigroups built from the character table of Abelian Groups that have an aperiodic flows.
title Aperiodic Flows on Finite Semigroups: Foundations and First Examples
topic Dynamical Systems
Group Theory
20M20, 20M35, 20M18
url https://arxiv.org/abs/2410.06668