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.