Quadratic mappings and Clifford algebras

Jacques Helmstetter, Artibano Micali3764386053, 9783764386054, 9783764386061

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.

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Table of contents :
Cover……Page 1
Quadratic Mappings and Clifford Algebras……Page 4
Copyright……Page 5
Contents……Page 6
Introduction……Page 9
1 Algebraic Preliminaries……Page 14
2 Quadratic Mappings……Page 66
3 Clifford Algebras……Page 117
4 Comultiplications. Exponentials. Deformations……Page 187
5 Orthogonal Groups and Lipschitz Groups……Page 242
6 Further Algebraic Developments……Page 334
7 Hyperbolic Spaces……Page 401
8 Complements about Witt Rings and Other Topics……Page 449
Bibliography……Page 499
Index of Definitions……Page 508
Index of Notation……Page 511