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Differential Geometry
Jacobi identity of Lie algebra intuition
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[QUOTE="fresh_42, post: 6586471, member: 572553"] The cross product only works for one special Lie algebra in 3 dimensions. The Jacobi identity remains to be the Leibniz rule in any dimension. There is no better way to describe it than by the formula $$ \operatorname{Ad}(\exp(A)) = \exp(\mathfrak{ad}(A)) $$ which directly connects the inner derivations of the tangent space (Jacobi) with the inner automorphisms of the group (conjugation). [/QUOTE]
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Jacobi identity of Lie algebra intuition
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