Affine Kac-Moody groups and Lie algebras in the language of SGA3

Abstract

In infinite-dimensional Lie theory, the affine Kac-Moody Lie algebras and groupsplay a distinguished role due to their many applications to various areas ofmathematics and physics. Underlying these infinite-dimensional objects there areclosely related group schemes and Lie algebras of finite type over Laurent polynomialrings. The language of SGA3 is perfectly suited to describe such objects. The purposeof this short article is to provide a natural description of the affine Kac-Moodygroups and Lie algebras using this language.