English

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.

Keywords

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

R2 v1 2026-06-23T21:57:23.585Z