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Research Article | Open Access

On the construction of Z2n−grassmannians as homogeneous Z2n−spaces

Mohammad Mohammadi( ), 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, Postal Code 45137-66731, Iran
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Abstract

In this paper, we construct the Z2n−grassmannians by gluing of the Z2n−domains and give an explicit description of the action of the Z2n−Lie group GL(m→) on the Z2n−grassmannian Gk→(m→) 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 Z2n−grassmannian.

Keywords

Z2n−Lie groupHomogeneous superspaceZ2n−manifoldZ2n− grassmannian

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Electronic Research Archive
Volume 30 Issue 1,
January 2022
Pages 221-241
DOI: 10.3934/era.2022012

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Cite this article:
Mohammadi M, Varsaie S. On the construction of Z2n−grassmannians as homogeneous Z2n−spaces. Electronic Research Archive, 2022, 30(1): 221-241. https://doi.org/10.3934/era.2022012

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Received: 23 May 2021
Revised: 05 September 2021
Accepted: 29 October 2021
Published: 15 January 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)