Semidirect product

Adjoining a derivation

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

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

Special cases

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

Footnotes

  1. 1988. Vertex operator algebras and the Monster, §1.3, p. 8 ↩