Commutative Post-Lie algebra structures on nilpotent Lie algebras and Poisson algebras

On the Kantor product, II

“…A commutative post-Lie structure on a Lie algebra (A, [, ]) is a bilinear product x • y that satisfy (see [5])…”

“…which gives the dual Leibniz rule (5) for {L i , L j , L m }. By similar calculation, we have the dual Leibniz rule (5) for {L i , L j , I m }, which conclude the proof of the statement.…”