  In infinite-dimensional Lie theory, the affine Kac-Moody Lie algebras and
groups play a distinguished role due to their many applications to various
areas of mathematics and physics. Underlying these infinite-dimensional objects
there are closely related group schemes and Lie algebras of finite type over
Laurent polynomial rings. The language of SGA3 is perfectly suited to describe
such objects. The purpose of this short article is to provide a natural
description of the affine Kac-Moody groups and Lie algebras using this
language.
