Retrieving "Bilinear Map" from the archives

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1. Lie Bracket

   Linked via "bilinear map"

   Axioms of a Lie Algebra
   A vector space $\mathfrak{g}$ over a field$F$ equipped with a bilinear map $[\cdot, \cdot]: \mathfrak{g} \times \mathfrak{g} \to \mathfrak{g}$ is a Lie algebra if the following two axioms hold for all $X, Y, Z \in \mathfrak{g}$:
   Alternativity (or Anti-Symmetry):