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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
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
Citation:
Andrew James Bruce, Eduardo Ibarguëngoytia, Norbert Poncin, “Linear $\mathbb{Z}_2^n$-Manifolds and Linear Actions”, SIGMA, 17 (2021), 060, 58 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1840 https://www.mathnet.ru/eng/sigma/v17/p60
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Abstract page: | 40 | Full-text PDF : | 18 | References: | 17 |
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