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arXiv · 1505.00955

Post-Lie algebra structures on pairs of Lie algebras

Dietrich Burde·Karel Dekimpe
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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.

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Dietrich Burde, Karel Dekimpe. 2016-06-24. Post-Lie algebra structures on pairs of Lie algebras. https://arxiv.org/abs/1505.00955

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