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- W760706684 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.
- W760706684 created "2016-06-24" @default.
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- W760706684 date "2015-05-05" @default.
- W760706684 modified "2023-09-23" @default.
- W760706684 title "Post-Lie algebra structures on pairs of Lie algebras" @default.
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