Every finite perfect two-sided skew brace decomposes as a central product of an almost trivial skew brace and a trivial skew brace, both arising from perfect groups, with perfectness equivalent for the brace and either underlying group.
Skew braces and the Yang-Baxter equa- tion
6 Pith papers cite this work. Polarity classification is still indexing.
6
Pith papers citing it
verdicts
UNVERDICTED 6representative citing papers
Compact connected simple Lie skew braces are rigid (trivial on S^1 or have simple groups and trivial/almost-trivial brace); all compact connected solvable ones are trivial, but noncompact simple examples with solvable groups exist.
The variety of skew braces is not action accessible.
Introduces left RG-semibraces from right groups to generate left non-degenerate set-theoretic Yang-Baxter equation solutions, properly generalizing left semibraces.
Proves solvability transfer from additive to multiplicative group in connected locally compact Hausdorff topological skew braces, with counterexamples omitting each hypothesis and rigidity when the additive group is abelian.
Classification and structural description of simple involutive latin solutions to the Yang-Baxter equation with regular displacement group and nilpotent permutation group, including enumeration for size p^p.
citing papers explorer
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On finite perfect two-sided skew braces
Every finite perfect two-sided skew brace decomposes as a central product of an almost trivial skew brace and a trivial skew brace, both arising from perfect groups, with perfectness equivalent for the brace and either underlying group.
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On simple compact Lie skew braces
Compact connected simple Lie skew braces are rigid (trivial on S^1 or have simple groups and trivial/almost-trivial brace); all compact connected solvable ones are trivial, but noncompact simple examples with solvable groups exist.
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Action accessibility in the variety of skew braces
The variety of skew braces is not action accessible.
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Right groups and the set-theoretic Yang-Baxter equation
Introduces left RG-semibraces from right groups to generate left non-degenerate set-theoretic Yang-Baxter equation solutions, properly generalizing left semibraces.
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Solvability and Rigidity for Topological Skew Braces
Proves solvability transfer from additive to multiplicative group in connected locally compact Hausdorff topological skew braces, with counterexamples omitting each hypothesis and rigidity when the additive group is abelian.
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Involutive (simple) latin solutions of the Yang-Baxter equation and related (left) quasigroups
Classification and structural description of simple involutive latin solutions to the Yang-Baxter equation with regular displacement group and nilpotent permutation group, including enumeration for size p^p.