Equality of DSER elementary orthogonal group and Eichler-Siegel-Dickson transvection group
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.
Publication Details
- Journal
- ArXiv.org
- Published
- 2025-03-17
- Primary Topic
- Holomorphic and Operator Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00