On dynamical skew braces and skew bracoids

2024/10/14 by Davide Ferri, Ferri, Davide · 1 citation
Mathematics · #16T25 #81R50 #FOS: Mathematics #Group Theory (math.GR) #Mathematics and Applications #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2410.10717

openalex publication_date 2024/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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.

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• Split Lemma and First Isomorphism Theorem for groupoids

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