Supergrassmannians as Homogeneous Superspaces

Abstract

A homogeneous space is a manifold on which a Lie group acts transitively. Super generalization of this concept is also studied in [2] and [4]. In this paper we explicitly show that super Lie group GL(m|n) acts transitively on supergrassmannian G_{k|l}(m|n). In this regard, by using functor of point approach, this action is constructed by gluing local actions.

23 pages

Cited by in corpus (1)

• On the Construction of ${\mathbb{Z}}_2^n-$Supergrassmannians as Homogeneous ${\mathbb{Z}}_2^n-$Superspaces