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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.12839 |
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| _version_ | 1866929761865957376 |
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| author | Pradeep, Gayathry Asokan, Ambily Ambattu Kovilakam, Aparna Pradeep Vadakke |
| author_facet | Pradeep, Gayathry Asokan, Ambily Ambattu Kovilakam, Aparna Pradeep Vadakke |
| contents | We prove the Dickson-Siegel-Eichler-Roy (DSER) elementary orthogonal group, which was introduced by Amit Roy in 1968 and the Eichler-Siegel-Dickson transvection group, which is in literature in the works of Dickson, Siegel and Eichler, are equal over a commutative ring in which $2$ is invertible. We prove the equality in the free case by considering the odd and even case separately and then generalize this result by using the local-global principle. This result generalizes previous results concerning the equality of elementary orthogonal transvection groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12839 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equality of DSER elementary orthogonal group and Eichler-Siegel-Dickson transvection group Pradeep, Gayathry Asokan, Ambily Ambattu Kovilakam, Aparna Pradeep Vadakke Commutative Algebra 19G99, 13C10, 11E70, 20H25 We prove the Dickson-Siegel-Eichler-Roy (DSER) elementary orthogonal group, which was introduced by Amit Roy in 1968 and the Eichler-Siegel-Dickson transvection group, which is in literature in the works of Dickson, Siegel and Eichler, are equal over a commutative ring in which $2$ is invertible. We prove the equality in the free case by considering the odd and even case separately and then generalize this result by using the local-global principle. This result generalizes previous results concerning the equality of elementary orthogonal transvection groups. |
| title | Equality of DSER elementary orthogonal group and Eichler-Siegel-Dickson transvection group |
| topic | Commutative Algebra 19G99, 13C10, 11E70, 20H25 |
| url | https://arxiv.org/abs/2503.12839 |