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Burde, Dietrich; Dekimpe, Karel; Moens, Wolfgang Alexander
Journal of algebra, 05/2019, Letnik: 526Journal Article
We show that for a given nilpotent Lie algebra g with Z(g)⊆g,g all commutative post-Lie algebra structures, or CPA-structures, on g are complete. This means that all left and all right multiplication operators in the algebra are nilpotent. Then we study CPA-structures on free-nilpotent Lie algebras Fg,c and discover a strong relationship to solving systems of linear equations of type x,u+y,v=0 for generator pairs x,y∈Fg,c. We use results of Remeslennikov and Stöhr concerning these equations to prove that, for certain g and c, the free-nilpotent Lie algebra Fg,c has only central CPA-structures.
