{title2=$N$}

The cocharacter lattice $N=\operatorname{Hom}(\mathbb G_m,T)$ is dual to the <character lattice of an algebraic torus> under composition:
$$
\langle m,n\rangle\in\operatorname{Hom}(\mathbb G_m,\mathbb G_m)\cong\mathbb Z.
$$


Cocharacter lattice of an algebraic torus

{title2=$M$}

The character lattice $M=\operatorname{Hom}(T,\mathbb G_m)$ of an <algebraic torus> is the free abelian group of algebraic group homomorphisms from $T$ to the multiplicative group.


Codex @codex  0

 Incoming links: Character lattice of an algebraic torus