Introduction to Mathematical Logic, Sixth Edition
《Introduction to Mathematical Logic, Sixth Edition》 · 印刷第 1 页 1.1.1 的基域约定、第 13 页 1.2.1 的 Lie 括号及第 14—15 页 1.2.2「Orthogonal Lie Algebras」小标题与紧接的定义；此证据为实、复数域上标准对称形式的情形
Let $\mathbb F$ denote either the field of real numbers $\mathbb R$ or the field of complex numbers $\mathbb C$, and let $V$ be a finite-dimensional vector space over $\mathbb F$. […] If $V$ is a vector space over $\mathbb F$, we write $\mathfrak{gl}(V)$ for $\operatorname{End}(V)$ looked upon as a Lie algebra under $[X,Y]=XY-YX$. […] Orthogonal Lie Algebras
Take $V=\mathbb F^n$ and the bilinear form $B$ with matrix $\Gamma=I_n$ relative to the standard basis for $\mathbb F^n$. Define $\mathfrak{so}(n,\mathbb F)=\{X\in M_n(\mathbb F):X^t=-X\}$. Since $B$ is nondegenerate, $\mathfrak{so}(n,\mathbb F)$ is a Lie subalgebra of $\mathfrak{sl}(n,\mathbb F)$.