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- W4297918162 abstract "We study post-Lie algebra structures on pairs of Lie algebras $(mathfrak{g},mathfrak{n})$, motivated by nil-affine actions of Lie groups. We prove existence results for such structures depending on the interplay of the algebraic structures of $mathfrak{g}$ and $mathfrak{n}$. We consider the classes of simple, semisimple, reductive, perfect, solvable, nilpotent, abelian and unimodular Lie algebras. Furthermore we consider commutative post-Lie algebra structures on perfect Lie algebras. Using Lie algebra cohomology we prove that such structures are trivial in several cases. We classify commutative structures on low-dimensional Lie algebras, and study the case of nilpotent Lie algebras." @default.
- W4297918162 created "2022-10-01" @default.
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- W4297918162 date "2015-05-05" @default.
- W4297918162 modified "2023-09-27" @default.
- W4297918162 title "Post-Lie algebra structures on pairs of Lie algebras" @default.
- W4297918162 doi "https://doi.org/10.48550/arxiv.1505.00955" @default.
- W4297918162 hasPublicationYear "2015" @default.
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