After general properties of quadratic mappings over rings, the authors more intensely study quadratic forms, and especially their Clifford algebras. To this purpose they review the required part of commutative algebra, and they present a significant part of the theory of graded Azumaya algebras. Interior multiplications and deformations of Clifford algebras are treated with the most efficient methods. The connection between orthogonal transformations and Cliffordalgebras is established in a new way, by means of Lipschitz monoids. Lipschitz monoids also allow a more efficient study of hyperbolic spaces. The study ofClifford algebras leads to sophisticated theories involving noncommutative algebras over a ring, e.g., Azumaya algebras, Morita theory, separability INDICE: Introduction.- 1. Algebraic Preliminaries.- 2. Quadratic Mappings.- 3. Clifford Algebras.- 4. Comultiplications. Exponentials. Deformations.- 5.Orthogonal Groups and Lipschitz Groups.- 6. Further Algebraic Developments.- 7. Hyperbolic Spaces.- 8. Other Topics.- Bibliography.- Index.
- ISBN: 978-3-7643-8605-4
- Editorial: Birkhaüser
- Encuadernacion: Cartoné
- Páginas: 400
- Fecha Publicación: 01/03/2008
- Nº Volúmenes: 1
- Idioma: Inglés
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- MATEMÁTICAS /
- ÁLGEBRA