Lie algebras MOC

Quadratic Lie algebra

A quadratic Lie algebra over 𝕂 consists of a Lie algebra 𝔤 over 𝕂 with a 𝔤-invariant symmetric linear form ⟨ ⋅, ⋅⟩ :𝔤 ×𝔤 →𝕂,¹ lie i.e. it is both a Lie algebra and a Quadratic space in a compatible way, namely

⟨[𝑥,𝑦],𝑧⟩=⟨𝑥,[𝑦,𝑧]⟩

See also

• Category of quadratic Lie algebras

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Footnotes

1. Away from 2 ↩