Adjoining a derivation

Let $𝔤$ be a Lie algebra over $𝕂$ and $𝑑$ be a derivation on $𝔤$ . Then one may adjoin the derivation $𝑑$ to $𝔤$ by taking the semidirect product #m/def/lie

𝔤 ⋊ 𝕂 𝑑

where $𝕂 𝑑$ is the free vector space generated by $𝑑$ with the unique (abelian) bracket.¹

Special cases

Adjoining the degree derivation

#state/develop | #lang/en | #SemBr

1988. Vertex operator algebras and the Monster, §1.3, p. 8 ↩

Adjoining a derivation

Special cases

Footnotes