Triangular Lie algebra

Triangular module

Let 𝔀 =π”«βˆ’ βŠ•π”₯ βŠ•π”«+ be a triangular Lie algebra over 𝕂 and πœ† :π”₯ →𝕂 be a linear form. The triangular module 𝑀(πœ†) is the induced 𝔀-module lie

𝑀(πœ†)=Ind𝔀π”₯βŠ•π”«+β‘π•‚πœ†

where the vacuum space π•‚πœ† =π•‚π‘£πœ† is the nonzero (π”₯ βŠ•π”«+)-module defined by1

𝔫+βŠ™π‘£πœ†=0β„ŽβŠ™π‘£πœ†=πœ†(β„Ž)π‘£πœ†

for β„Ž ∈π”₯. This is a direct generalization of the Heisenberg module 𝑀(π‘˜).

Properties


tidy | en | SemBr

Footnotes

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