Conjugacy of Isometries in Real Orthogonal Groups

TL;DR

This paper characterizes specific orthogonal transformations in real quadratic spaces that maintain conjugacy relations within the orthogonal group, providing a detailed classification of such transformations.

Contribution

It identifies all orthogonal transformations whose conjugacy relations in the linear group are preserved within the orthogonal group, a novel classification result.

Findings

Characterization of orthogonal transformations with conjugacy preservation

Complete classification of such transformations in real quadratic spaces

Insights into conjugacy relations within orthogonal groups

Abstract

We determine all orthogonal transformations of a quadratic space over reals such that any orthogonal transformation which is conjugate to one of them in the linear group is conjugate in the orthogonal group.