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 Gk|l(m|n). In this regard, by using functor of point approach, this action is constructed by gluing local actions.
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