Orthogonal Groups and Lipschitz Groups


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 aM 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)).


Local Ring Direct Summand Orthogonal Group Projective Module Orthogonal Transformation 
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© Birkhäuser Verlag AG 2008

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