Triangular Lie algebra

Triangular module

Let 𝔤 =𝔫− ⊕𝔥 ⊕𝔫+ be a triangular Lie algebra over 𝕂 and 𝜆 :𝔥 →𝕂 be a linear form. The triangular module 𝑀(𝜆) is the induced 𝔤-module #m/def/lie

where the vacuum space 𝕂𝜆 =𝕂𝑣𝜆 is the nonzero (𝔥 ⊕𝔫+)-module defined by¹

for ℎ ∈𝔥. This is a direct generalization of the Heisenberg module 𝑀(𝑘).

Properties

• Contravariant form on a triangular module

#state/tidy | #lang/en | #SemBr