Abstract
In this paper, we introduce the notion of a Minkowski Lie algebra, which is the natural generalization of the notion of a real quadratic Lie algebra (metric Lie algebra). We then study the positive definite Minkowski Lie algebras and obtain a complete classification of the simple ones. Finally, we present some applications of our results to Finsler geometry and give a classification of bi-invariant Finsler metrics on Lie groups.
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