Super Lie groups: global topology and local structure

Abstract

A general mathematical framework for the super Lie groups of supersymmetric theories is presented. The definition of super Lie group is given in terms of supermanifolds, and two theorems (analogous to theorems in classical Lie group theory) are proved. The relationship of the super Lie groups defined here to the formal groups of Berezin and Kac and the graded Lie groups of Kostant is analyzed.