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Let G a four dimmensionnal Lie group with g as lie algebra. Let T1 ... T4 the four generator. I would like to find à lorentzian scalar product (1-3 Signature) on it and left invariant. A classical algebra take tr (AB^t) as scalar product but I don't find à lorentzian équivalent. Did it contraint the generator or the structure constant to respect some criterion ?

Thanks for your answer

Clement

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# Lorentzian lie algebra

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