Cayley parametrization and the rotation group over a non-archimedean pythagorean field

TL;DR

This paper explores the use of Cayley transform to construct rotation matrices close to the identity over non-archimedean pythagorean fields and applies this to build specific subgroups of the rotation group.

Contribution

It introduces a novel method using Cayley transform for constructing near-identity rotations and provides an alternative approach to subgroup construction in this setting.

Findings

Constructed rotation matrices near the identity using Cayley transform

Provided an alternative method for constructing non-central proper normal subgroups

Extended the understanding of rotation groups over non-archimedean pythagorean fields

Abstract

Using Cayley transform, we show how to construct rotation matrices \emph{infinitely near} the identity matrix over a non-archimedean pythagorean field. As an application, an alternative way to construct non-central proper normal subgroups of the rotation group over such fields is provided.