- Date
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Tuesday 17 December 2024, 11.30 - 12.00
- Abstract
- The skew bracoid and the semi-brace are generalisations of the skew brace, proposed separately and with links to different areas of study. The former has the multiplicative and additive groups on potentially distinct underlying sets, while the latter allows the additive structure to be merely a left cancellative semigroup. We show that a large family of skew bracoids are in correspondence with semi- braces, thus connecting semi-braces to Hopf-Galois structures on separable extensions of fields and, as we explore in this talk, skew bracoids to solutions to the set-theoretic Yang-Baxter equation.
