Lie supergroups and principal superfibre bundles

Abstract

This last Chapter is devoted to developing the rudiments of a theory of Lie supergroups within the category of G-supermanifolds, together with the basic definitions related to principal superfibre bundles and associated superbundles. Since a G-supermanifold structure is not determined by the underlying topological space, the group axioms must be expressed in categorial terms.¹ This is what happens in the theory of algebraic groups, whose guidelines will be followed here. Most of our material will be taken, with the necessary modifications, from [Wat, Hum], where the theory of algebraic groups is developed, from [Pen], containing the theory of Lie supergroups and their representations in the context of algebraic graded manifolds (superschemes), and from [Lop], which is devoted to graded Lie groups (i.e., Lie groups in the framework of the Berezin-Leĭtes-Kostant graded manifold theory, as earlier considered in [Kos]).

Y ¿qué importa errar lo menos quien ha accertado lo más ? P. Calderón De La Barca