Orthogonal Groups and Lipschitz Groups

Abstract

In this chapter, M is a K-module provided with a cliffordian quadratic form q; according to Definition (4.8.1), this means that the canonical mappings K → Cℓ(M,q) and M → Cℓ(M,q) are injective; thus the unit element 1 _q of Cℓ(M,q) is identified with the unit element 1 of K, and every a ∈ M is identified with its image ρ(a) in Cℓ(M,q); from now on, these identifications are done without warning. The existence of an admissible scalar product β (see (4.8.6)) is still the only available general criterion allowing us to recognize whether a quadratic form is cliffordian (see (4.8.7)).