Post-Lie Algebra Structures and Generalized Derivations of Semisimple Lie Algebras

摘要

We study post-Lie algebra structures on pairs of Lie algebras (g,n), andprove existence results for the case that one of the Lie algebras issemisimple. For semisimple g and solvable n we show that there exist nopost-Lie algebra structures on (g,n). For semisimple n and certain solvable gwe construct canonical post-Lie algebra structures. On the other hand we provethat there are no post-Lie algebra structures for semisimple n and solvable,unimodular g. We also determine the generalized $(l,e,ga)$-derivations ofn in the semisimple case. As an application we classify post-Lie algebrastructures induced by generalized derivations.