Torsors in super-symmetry
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866916455476363264 |
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| author | Masuoka, Akira Oe, Takuya Takahashi, Yuta |
| author_facet | Masuoka, Akira Oe, Takuya Takahashi, Yuta |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_03461 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Torsors in super-symmetry Masuoka, Akira Oe, Takuya Takahashi, Yuta Algebraic Geometry 14L15, 14M30, 16T05 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. |
| title | Torsors in super-symmetry |
| topic | Algebraic Geometry 14L15, 14M30, 16T05 |
| url | https://arxiv.org/abs/2101.03461 |