English

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

Commutative Algebra 2025-03-18 v1

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 22 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.

Keywords

Cite

@article{arxiv.2503.12839,
  title  = {Equality of DSER elementary orthogonal group and Eichler-Siegel-Dickson transvection group},
  author = {Gayathry Pradeep and Ambily Ambattu Asokan and Aparna Pradeep Vadakke Kovilakam},
  journal= {arXiv preprint arXiv:2503.12839},
  year   = {2025}
}