Character lattice of an algebraic torus ($M$)

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

An algebraic torus character is a morphism of algebraic groups $T\to {\mathbb{G}}_m$. For a split torus with character lattice $M$, these are precisely the Laurent monomials ${\chi }^m$, with ${\chi }^{m+m^{\prime }}={\chi }^m{\chi }^{m^{\prime }}$.

// Target: algebra.bigb