Triangular Lie algebra Triangular module Let π€ =π«β βπ₯ βπ«+ be a triangular Lie algebra over π and π :π₯ βπ be a linear form. The triangular module π(π) is the induced π€-module lie π(π)=Indπ€π₯βπ«+β‘ππ where the vacuum space ππ =ππ£π is the nonzero (π₯ βπ«+)-module defined by1 π«+βπ£π=0ββπ£π=π(β)π£π for β βπ₯. This is a direct generalization of the Heisenberg module π(π). Properties Contravariant form on a triangular module tidy | en | SemBr Footnotes 1988. Vertex operator algebras and the Monster, Β§1.8, p. 26 β©