On the Construction of ℤ₂ⁿ-Supergrassmannians as Homogeneous ℤ₂ⁿ-Superspaces

2019/01/18 by Mohammadi, Mohammad, Varsaie, Saad
#20N99 #58A50 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1901.07393

Abstract

In this paper, we construct the \mathbb Z₂ⁿ-supergrassmannians by gluing of the \mathbb Z₂ⁿ-superdomains and give an explicit description of the action of the \mathbb Z₂ⁿ-super Lie group GL(\overrightarrowm) on the \mathbb Z₂ⁿ-supergrassmannian G_\overrightarrowk(\overrightarrowm) in the functor of points language. In particular, we give a concrete proof of the transitively of this action, and the gluing of the local charts of the supergrassmannian.

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