MathGloss

Let $(L,F)$ be a vector space with a binary operation $L\times L \to L$ denoted $(x,y) \mapsto [xy]$. This operation is called the bracket or commutator of $x$ and $y$. The vector space together with the operation is a Lie algebra over the field $F$ if

1. The bracket operation is bilinear;
2. $[xx] = 0$ for all $x \in L$;
3. $[xyz + [yzx+[zxy =0$ for all $x,y,z\in L$.

The last axiom is called the Jacobi identity.

Wikidata ID: Q664495

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