Quadratic Lie algebra

Category of quadratic Lie algebras

The category of quadratic Lie algebras 𝖰𝖫𝗂𝖾𝕂 is a category where an object is a Quadratic Lie algebra over 𝕂 and a morphism is a isometric Lie algebra homomorphism. lie Thus if 𝑓 ∈𝖰𝖫𝗂𝖾𝕂(𝔤,𝔥) then

⟨𝑓(𝑥),𝑓(𝑦)⟩𝔥=⟨𝑥,𝑦⟩𝔤

for any 𝑥,𝑦 ∈𝔤.

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