The Super Lie Groups Associated to Odd Involutions

Abstract

A new generalization of Grassmannians in supergeometry, called $\nu-$Grassmannians, are constructed by gluing $\nu-$domains. By a $\nu-$domain, we mean a superdomain with an odd involution say $\nu$ on its structure sheaf, as morphism of modules. Then we show that $\nu-$Grassmannians are homogeneous superspaces. In addition, in the last section, a supergroup associated to the odd involution $\nu$ is introduced.