On dynamical skew braces and skew bracoids

Fuente: arXiv
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Main Author: Ferri, Davide
Format: Preprint
Published: 2024
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author Ferri, Davide
author_facet Ferri, Davide
contents Dynamical skew braces are known to produce solutions to the quiver-theoretic Yang--Baxter equation. Under a technical hypothesis, we prove that these solutions are braided groupoids (and hence skew bracoids in the sense of Sheng, Tang and Zhu). Conversely, every connected braided groupoid can be parallelised, making it isomorphic to a dynamical skew brace. We study the combinatorics of these objects, depending on some strings of integer invariants.
format Preprint
id arxiv_https___arxiv_org_abs_2410_10717
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On dynamical skew braces and skew bracoids
Ferri, Davide
Quantum Algebra
Group Theory
16T25, 81R50
Dynamical skew braces are known to produce solutions to the quiver-theoretic Yang--Baxter equation. Under a technical hypothesis, we prove that these solutions are braided groupoids (and hence skew bracoids in the sense of Sheng, Tang and Zhu). Conversely, every connected braided groupoid can be parallelised, making it isomorphic to a dynamical skew brace. We study the combinatorics of these objects, depending on some strings of integer invariants.
title On dynamical skew braces and skew bracoids
topic Quantum Algebra
Group Theory
16T25, 81R50
url https://arxiv.org/abs/2410.10717