Geometries of orthogonal groups and their contractions: a unified classical deformation viewpoint

TL;DR

This paper explores the geometries associated with real orthogonal groups and their contractions, providing a unified classical deformation perspective, including explicit descriptions of central extensions, Casimirs, and an approach to their trigonometry.

Contribution

It offers a unified framework for understanding the geometries of orthogonal groups and their contractions through classical deformation theory, with explicit algebraic and geometric characterizations.

Findings

Explicit descriptions of central extensions and Casimirs for these geometries

A unified classical deformation approach to orthogonal group geometries

Advancement in the trigonometry of these spaces

Abstract

The geometries of spaces having as groups the real orthogonal groups and some of their contractions are described from a common point of view. Their central extensions and Casimirs are explicitly given. An approach to the trigonometry of their spaces is also advanced.