3 research outputs found
Post-Lie algebra structures for perfect Lie algebras
We study the existence of post-Lie algebra structures on pairs of Lie
algebras , where one of the algebras is perfect
non-semisimple, and the other one is abelian, nilpotent non-abelian, solvable
non-nilpotent, simple, semisimple non-simple, reductive non-semisimple or
complete non-perfect. We prove several non-existence results, but also provide
examples in some cases for the existence of a post-Lie algebra structure. Among
other results we show that there is no post-Lie algebra structure on
, where is perfect non-semisimple,
and is . We also show that there is
no post-Lie algebra structure on , where
is perfect and is reductive with a
-dimensional center