Introduction to Lie Algebras and Representation Theory
《Introduction to Lie Algebras and Representation Theory》 · 第 1 页 · Section 1.1「The notion of Lie algebra」，Definition
A vector space $L$ over a field $F$, with an operation $L\times L\to L$, denoted $(x,y)\mapsto[xy]$ and called the bracket or commutator of $x$ and $y$, is called a Lie algebra over $F$ if the following axioms are satisfied: (L1) The bracket operation is bilinear. (L2) $[xx]=0$ for all $x$ in $L$. (L3) $[x[yz]]+[y[zx]]+[z[xy]]=0$ $(x,y,z\in L)$.