character

《Naive Lie Theory》 · 印刷第 21 页 Chapter 2 章首域的约定、第 23 页 2.1.4(2) 乘法群记号、第 43 页 Section 3.2「Diagonalizable groups and tori」，3.2.1 特征标定义（省略中间内容）

$k$ is an algebraically closed field and $F$ a subfield. All algebraic varieties are over $k$. […] (2) $G=\mathbf A^1-\{0\}=k^*$, with multiplication as group operation. […] This algebraic group is denoted by $\mathbf G_m$ or by $\mathbf{GL}_1$; it is the multiplicative group. […] Let $G$ be a linear algebraic group. A homomorphism of algebraic groups $\chi:G\to\mathbf G_m$ is called a rational character (or simply a character).