arXiv Open Access 2024

Aperiodic Flows on Finite Semigroups: Foundations and First Examples

Stuart Margolis John Rhodes

Lihat Sumber

Abstrak

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.

Topik & Kata Kunci

math.DS math.GR

Penulis (2)

Stuart Margolis

John Rhodes

Format Sitasi

APA MLA BibTeX

Margolis, S., Rhodes, J. (2024). Aperiodic Flows on Finite Semigroups: Foundations and First Examples. https://arxiv.org/abs/2410.06668

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓