Post-Lie algebra structures on pairs of Lie algebras

© 2016 Elsevier Inc. We study post-Lie algebra structures on pairs of Lie algebras (g,n), which describe simply transitive nil-affine actions of Lie groups. We prove existence results for such structures depending on the interplay of the algebraic structures of g and 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 can classify such structures in several cases. We also study commutative structures on low-dimensional Lie algebras and on nilpotent Lie algebras.

Publication year:2016

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CSS-citation score:3

Authors:International

Authors from:Higher Education