Naive Lie Theory
《Naive Lie Theory》 · 印刷第 21 页 Chapter 2 章首域的约定、2.1.1 的群乘法与求逆记号、2.1.2 的坐标环结构映射定义（省略中间内容）
$k$ is an algebraically closed field and $F$ a subfield. All algebraic varieties are over $k$. […] An algebraic group is an algebraic variety $G$ which is also a group such that the maps defining the group structure $\mu:G\times G\to G$ with $\mu(x,y)=xy$ and $i:x\mapsto x^{-1}$ are morphisms of varieties. […] Let $G$ be a linear algebraic group and put $A=k[G]$. By 1.4.7 the morphisms $\mu$ and $i$ are defined by an algebra homomorphism $\Delta:A\to A\otimes_k A$ (called comultiplication) and an algebra isomorphism $\iota:A\to A$ (called antipode).