CHAPTER 2

Projective and Affine Geometry over Division Rings

Francis BUEKENHOUT

CP 216, Université Libre de Bruxelles, Boulevard du Triomphe, B-1050 Bruxelles, Belgium

Peter CAMERON

Queen Mary and Westfield College, Miles End Road, London E1 4NS, UK

Contents

Introduction

1. Projective and affine spaces

2. Axiomatizations

3. Collineations and correlations

4. Polar spaces

5. Buekenhout geometries

6. Grassmannians

7. Clifford algebras and spinors

8. Finite geometries

9. The projective line

References