Lie algebras MOC

Triangular Lie algebra

Let 𝔤 be a Lie algebra over 𝕂. A triangular decomposition of 𝔤 is a triple of subalgebras 𝔫±,𝔥 ≤𝔤 such that

𝔤=𝔫−⊕𝔥⊕𝔫+

where 𝔥 is abelian and [𝔥,𝔫±] ⊆𝔫±.¹ 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

• Special linear Lie algebra

---

tidy | en | SemBr

Footnotes

1. 1988. Vertex operator algebras and the Monster, §1.8, p. 26 ↩