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
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article

Equality of DSER elementary orthogonal group and Eichler-Siegel-Dickson transvection group

ArXiv.org
Holomorphic and Operator Theory
article

Equality of DSER elementary orthogonal group and Eichler-Siegel-Dickson transvection group

article en

Abstract

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.

ArXiv.org
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Holomorphic and Operator Theory
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Equality of DSER elementary orthogonal group and Eichler-Siegel-Dickson transvection group · ArXiv.org (2025) | TGRS Research Map | TGRS