Triangular Lie algebra

Let $𝔤$ be a Lie algebra over $𝕂$ . A triangular decomposition of $𝔤$ is a triple of subalgebras $𝔫 \pm, 𝔥 \leq 𝔤$ such that

𝔤 = 𝔫 - \oplus 𝔥 \oplus 𝔫 +

where $𝔥$ is abelian and $[𝔥, 𝔫 \pm] \subseteq 𝔫 \pm$ .¹ #m/def/lie A Lie algebra with such a decomposition is called triangular. This may be viewed as a generalization of a Heisenberg algebra.

Properties

Triangular module
Contravariant form on a triangular module

Examples

$𝔰 𝔩 𝑛 𝕂$

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

1988. Vertex operator algebras and the Monster, §1.8, p. 26 ↩

Triangular Lie algebra

Properties

Examples

Footnotes