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On the construction of supergrassmannians as homogeneous superspaces

Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), No. 444, Prof. Yousef Sobouti Blvd. P. O. Box 45195-1159, Zanjan, Iran, Postal Code 45137-66731, Iran

E-mail Address: moh.mohamady@iasbs.ac.ir

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and

Saad Varsaie

Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), No. 444, Prof. Yousef Sobouti Blvd. P. O. Box 45195-1159, Zanjan, Iran, Postal Code 45137-66731, Iran

E-mail Address: varsaie@iasbs.ac.ir

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https://doi.org/10.1142/S1793557121500534Cited by:2 (Source: Crossref)

Abstract

In this paper, we give an explicit description of the action of the super Lie group $GL (m | n)$ on supergrassmannian $G_{k | l} (m | n)$ 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.

Communicated by L. A. Bokut

Keywords:

AMSC: Primary: 58A50, Secondary: 20N99

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