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Torsors in super-symmetry. arXiv:2101.03461

Preprint, arXiv:2101.03461 [math.AG] (2021).
Summary: Torsors under affine groups are generalized in the super context by super-torsors under affine super-groups. We investigate those super-torsors by using Hopf-algebra language and techniques. It is explicitly shown, under suitable assumptions, that every super-torsor arises from an ordinary torsor. Especially, the objects with affinity restriction, or namely, the affine super-torsors and the affine ordinary torsors are shown to be precisely in one-to-one correspondence. The results play substantial roles in ongoing construction of super-symmetric Picard-Vessiot theory.

MSC:

14L15 Group schemes
14M30 Supervarieties
16T05 Hopf algebras and their applications
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