Super Distributions, Analytic and Algebraic Super Harish-Chandra pairs

The purpose of this paper is to extend the theory of Super Harish-Chandra pairs, originally developed by Koszul for Lie supergroups, to analytic and algebraic supergroups, in order to obtain information also about their representations. We also define the distribution superalgebra for algebraic and analytic supergroups and study its relation with the universal enveloping superalgebra