Torsors in super-symmetry
Algebraic Geometry
2024-10-29 v5
Abstract
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.
Cite
@article{arxiv.2101.03461,
title = {Torsors in super-symmetry},
author = {Akira Masuoka and Takuya Oe and Yuta Takahashi},
journal= {arXiv preprint arXiv:2101.03461},
year = {2024}
}
Comments
Final version to be published in J. Noncom. Geometry. Minor changes made to the last version; corrected some typos and changed some English expressions