2011/08/30 by Dietrich Burde, Burde, Dietrich, Karel Dekimpe +1 · 2 citations
Mathematics · #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1108.5950
openalex publication_date 2011/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study post-Lie algebra structures on pairs of Lie algebras (g,n), and\nprove existence results for the case that one of the Lie algebras is\nsemisimple. For semisimple g and solvable n we show that there exist no\npost-Lie algebra structures on (g,n). For semisimple n and certain solvable g\nwe construct canonical post-Lie algebra structures. On the other hand we prove\nthat there are no post-Lie algebra structures for semisimple n and solvable,\nunimodular g. We also determine the generalized ( al, be, ga)-derivations of\nn in the semisimple case. As an application we classify post-Lie algebra\nstructures induced by generalized derivations.\n