Albert algebras provide key tools for understanding exceptional groups and related structures such as symmetric spaces. This self-contained book provides the first comprehensive reference on Albert algebras over fields without any restrictions on the characteristic of the field. As well as covering results in characteristic 2 and 3, many results are proven for Albert algebras over an arbitrary commutative ring, showing that they hold in this greater generality. The book extensively covers requisite knowledge, such as non-associative algebras over commutative rings, scalar extensions, projective modules, alternative algebras, and composition algebras over commutative rings, with a special focus on octonion algebras. It then goes into Jordan algebras, Lie algebras, and group schemes, providing exercises so readers can apply concepts. This centralized resource illuminates the interplay between results that use only the structure of Albert algebras and those that employ theorems about group schemes, and is ideal for mathematics and physics researchers.
Les mer
I. Prologue: the ancient protagonists; II. Foundations; III. Alternative algebras; IV. Composition algebras; V. Jordan algebras; VI. Cubic Jordan algebras; VII. The two Tits constructions; VIII. Lie algebras; IX. Group schemes; References; Index of notation; Subject index.
Les mer
The first comprehensive book on Albert algebras, the Jordan algebras that are most important for Lie algebras and exceptional groups.
Produktdetaljer
ISBN
9781009426855
Publisert
2024-11-21
Utgiver
Vendor
Cambridge University Press
Vekt
1193 gr
Høyde
229 mm
Bredde
152 mm
Dybde
37 mm
Aldersnivå
UP, 05
Språk
Product language
Engelsk
Format
Product format
Innbundet
Antall sider
677