Commutative post-Lie Algebra Structures Research Articles

Commutative post-Lie algebra structures on Lie algebras

We show that any CPA-structure (commutative post-Lie algebra structure) on a perfect Lie algebra is trivial. Furthermore we give a general decomposition of inner CPA-structures, and classify all CPA-structures on complete Lie algebras. As a special case we obtain the CPA-structures of parabolic subalgebras of semisimple Lie algebras.

Post-Lie algebra structures on pairs of Lie algebras

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.