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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2 Pith papers cite this work. Polarity classification is still indexing.
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2026 2verdicts
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Analogues of Sylow's first, Cauchy's, and Hall's theorems are established for finite skew braces, with application to classification of order pq examples.
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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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Analogues of Sylow's first theorem, Cauchy's theorem, and Hall's theorem for skew braces
Analogues of Sylow's first, Cauchy's, and Hall's theorems are established for finite skew braces, with application to classification of order pq examples.