Super G-spaces
Luigi Balduzzi, Claudio Carmeli, Gianni Cassinelli

TL;DR
This paper reviews super G-spaces, proves a key theorem relating super Harish-Chandra pairs to super Lie group actions, and establishes the representability of the stability subgroup functor, advancing the theoretical framework of supergeometry.
Contribution
It provides a proof of a theorem connecting super Harish-Chandra pairs and super Lie group actions without using Frobenius theorem, using Koszul realization.
Findings
Proved the theorem relating super Harish-Chandra pairs to super Lie group actions.
Established the representability of the stability subgroup functor.
Provided a proof avoiding Frobenius theorem, using Koszul realization.
Abstract
We review the basic theory of super -spaces. We prove a theorem relating the action of a super Harish-Chandra pair on a supermanifold to the action of the corresponding super Lie group . The theorem was stated in [DM99] without proof. The proof given here does not use Frobenius theorem but relies on Koszul realization of the structure sheaf of a super Lie group (see [Kosz83]). We prove the representability of the stability subgroup functor.
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Taxonomy
TopicsFuzzy and Soft Set Theory
