Non-abelian extensions and automorphisms of post-Lie algebras

In this paper, we introduce the concepts of crossed modules of post-Lie algebras and cat^1-post-Lie algebras. It is proved that these two concepts are equivalent to each other. We also construct a non-abelian cohomology for post-Lie algebras to classify their nonabelian extensions. At last, we investigate the inducibility of a pair of automorphisms for post-Lie algebras and construct a Wells-type exact sequence.