Algebraic one-parameter subgroup
= Algebraic one-parameter subgroup
{title2=$\lambda:\mathbb G_m\to G$}
An algebraic one-parameter subgroup is a regular group homomorphism from the multiplicative algebraic group. In $SL_n$, a change of basis makes it $t\mapsto\operatorname{diag}(t^{a_1},\ldots,t^{a_n})$ for integers with sum zero. This is the algebraic multiplicative notion, distinct from an additive real-parameter subgroup of a Lie group.