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Symmetry, Integrability and Geometry: Methods and Applications, 2021, Volume 17, 060, 58 pp.
DOI: https://doi.org/10.3842/SIGMA.2021.060
(Mi sigma1840)
 

This article is cited in 4 scientific papers (total in 4 papers)

Linear $\mathbb{Z}_2^n$-Manifolds and Linear Actions

Andrew James Bruce, Eduardo Ibarguëngoytia, Norbert Poncin

Department of Mathematics, University of Luxembourg, Maison du Nombre, 6, avenue de la Fonte, L-4364 Esch-sur-Alzette, Luxembourg
Full-text PDF (787 kB) Citations (4)
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Abstract: We establish the representability of the general linear $\mathbb{Z}_2^n$-group and use the restricted functor of points – whose test category is the category of $\mathbb{Z}_2^n$-manifolds over a single topological point – to define its smooth linear actions on $\mathbb{Z}_2^n$-graded vector spaces and linear $\mathbb{Z}_2^n$-manifolds. Throughout the paper, particular emphasis is placed on the full faithfulness and target category of the restricted functor of points of a number of categories that we are using.
Keywords: supergeometry, ringed spaces, functors of points, linear group actions.
Received: November 5, 2020; in final form May 30, 2021
Bibliographic databases:
Document Type: Article
Language: English
Citation: Andrew James Bruce, Eduardo Ibarguëngoytia, Norbert Poncin, “Linear $\mathbb{Z}_2^n$-Manifolds and Linear Actions”, SIGMA, 17 (2021), 060, 58 pp.
Citation in format AMSBIB
\Bibitem{BruIbaPon21}
\by Andrew~James~Bruce, Eduardo~Ibargu\"engoytia, Norbert~Poncin
\paper Linear $\mathbb{Z}_2^n$-Manifolds and Linear Actions
\jour SIGMA
\yr 2021
\vol 17
\papernumber 060
\totalpages 58
\mathnet{http://mi.mathnet.ru/sigma1840}
\crossref{https://doi.org/10.3842/SIGMA.2021.060}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85107923320}
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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    Abstract page:39
    Full-text PDF :18
    References:17
     
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