Post-Lie algebra structures and generalized derivations of semisimple Lie algebras

Details Post-Lie algebra structures and generalized derivations of semisimple Lie algebras Post-Lie algebra structures and generalized derivations of semisimple Lie algebras

2011-08-30

arxiv.org/abs/1108.5950v1

Mathematics

Rings and Algebras

Scientific paper

We study post-Lie algebra structures on pairs of Lie algebras (g,n), and prove existence results for the case that one of the Lie algebras is semisimple. For semisimple g and solvable n we show that there exist no post-Lie algebra structures on (g,n). For semisimple n and certain solvable g we construct canonical post-Lie algebra structures. On the other hand we prove that there are no post-Lie algebra structures for semisimple n and solvable, unimodular g. We also determine the generalized $(\al,\be,\ga)$-derivations of n in the semisimple case. As an application we classify post-Lie algebra structures induced by generalized derivations.

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