Semidirect product Adjoining a derivation Let π€ be a Lie algebra over π and π be a derivation on π€. Then one may adjoin the derivation π to π€ by taking the semidirect product lie π€βππ where ππ is the free vector space generated by π with the unique (abelian) bracket.1 Special cases Adjoining the degree derivation develop | en | SemBr Footnotes 1988. Vertex operator algebras and the Monster, Β§1.3, p. 8 β©