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

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.

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Cited by in corpus (4)

• Irreducible representations of ${\mathbb{Z}}_2^2$-graded $\mathcal{N}=2$ supersymmetry algebra and ${\mathbb{Z}}_2^2$-graded supermechanics
• Integration on minimal ${\mathbb{Z}}_2^2$-superspace and emergence of space
• Local Forms of Morphisms of Colored Supermanifolds
• ${\mathbb{Z}}_2^2$-graded supersymmetry via superfield on minimal ${\mathbb{Z}}_2^2$-superspace