- algebra, higher algebra
- universal algebra
- monoid, semigroup, quasigroup
- nonassociative algebra
- associative unital algebra
- commutative algebra
- Lie algebra, Jordan algebra
- Leibniz algebra, pre-Lie algebra
- Poisson algebra, Frobenius algebra
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- distributive law

- group, normal subgroup
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A *skew brace* is a set equipped with a pair of group structures satisfying some compatibility conditions.

This is a generalization of the concept of *brace* (an algebraic structure due W. Rump), which it reduces to when one of the groups is Abelian.

Skew baces can be used to construct solutions to the set-theoretic Yang-Baxter equation; their actions can be used to construct solutions of the reflection equation.

Introduced in

- L. Guarnieri, L. Vendramin,
*Skew braces and the Yang–Baxter equation*, Math. Comp.**86**(2017) 2519–2534 doi

Viewpoint via sup-lattices

- Aryan Ghobadi,
*Skew braces as remnants of co-quasitriangular Hopf algebras in SupLat*, J. Algebra**586**(2021) 607–642 doi

In construction of solutions to set-theoretic Yang–Baxter equation,

- Valeriy G. Bardakov, Vsevolod Gubarev,
*Rota–Baxter groups, skew left braces, and the Yang–Baxter equation*, Journal of Algebra**596**(2022) 328–351 doi

In construction of solutions of the reflection equation

- Kenny De Commer,
*Actions of skew braces and set-theoretic solutions of the reflection equation*, Proc. Edinburgh Math. Soc.**62**:4 (2019) 1089–1113 doi

category: algebra

Last revised on October 1, 2024 at 11:32:07. See the history of this page for a list of all contributions to it.