Lie algebras MOC

Triangular Lie algebra

Let be a Lie algebra over . A triangular decomposition of is a triple of subalgebras such that

where is abelian and .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

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Footnotes

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