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.

17 pages. arXiv admin note: text overlap with arXiv:1801.02159