Almost classical skew bracoids
Isabel Martin-Lyons

TL;DR
This paper studies special subclasses of skew bracoids called almost a brace and almost classical, exploring their structure and applications in Hopf-Galois theory and solutions to the Yang-Baxter equation.
Contribution
It introduces a new perspective on skew bracoids, providing constructions, recovering known results, and analyzing solutions related to the Hopf-Galois correspondence.
Findings
New construction based on induced Hopf-Galois structures
Recovered Greither and Pareigis' result on Hopf-Galois correspondence
Analyzed solutions arising from skew bracoids, including multiple solutions from one skew bracoid
Abstract
We investigate two sub-classes of skew bracoids, the first consists of those we term almost a brace, meaning the multiplicative group decomposes as a certain semi-direct product, and then those that are almost classical, which additionally specifies the relationship between the multiplicative group and the additive. Skew bracoids with these properties have applications in Hopf-Galois theory, in particular for questions concerning the Hopf-Galois correspondence, and can also yield solutions to the set-theoretic Yang-Baxter equation. We use this skew bracoid perspective to give a new construction building on the induced Hopf-Galois structures of Crespo, Rio and Vela, recover a result of Greither and Pareigis on the Hopf-Galois correspondence, and examine the solutions that arise from skew bracoids, in particular where more than one solution may be drawn from a single skew bracoid.
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Taxonomy
TopicsMathematics and Applications · Fuzzy and Soft Set Theory · Biological Activity of Diterpenoids and Biflavonoids
