Quadratic Mappings and Clifford Algebras [electronic resource] / by Jacques Helmstetter, Artibano Micali.

Algebraic Preliminaries -- Quadratic Mappings -- Clifford Algebras -- Comultiplications. Exponentials. Deformations -- Orthogonal Groups and Lipschitz Groups -- Further Algebraic Developments -- Hyperbolic Spaces -- Complements about Witt Rings and Other Topics.

After a classical presentation of quadratic mappings and Clifford algebras over arbitrary rings (commutative, associative, with unit), other topics involve more original methods: interior multiplications allow an effective treatment of deformations of Clifford algebras; the relations between automorphisms of quadratic forms and Clifford algebras are based on the concept of the Lipschitz monoid, from which several groups are derived; and the Cartan-Chevalley theory of hyperbolic spaces becomes much more general, precise and effective.