In connected locally compact Hausdorff topological skew braces, solvability of the additive group forces solvability of the multiplicative group, with the two operations coinciding when the additive group is abelian and the brace is compact.
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2 Pith papers cite this work. Polarity classification is still indexing.
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math.GR 2years
2026 2verdicts
UNVERDICTED 2representative 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.
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Solvability and Rigidity for Topological Skew Braces
In connected locally compact Hausdorff topological skew braces, solvability of the additive group forces solvability of the multiplicative group, with the two operations coinciding when the additive group is abelian and the brace is compact.
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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.