Albert Algebras over Commutative Rings
Albert Algebras over Commutative Rings
Holger P. Petersson, FernUniversität in Hagen
Michel L. Racine, University of Ottawa
$205.00
USDAlbert 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.
- Facilitates active learning by introducing complementary material in exercises
- Provides a guide to the literature by centralizing major results
- Equips future study of algebraic problems not yet well understood over rings
Product details
November 2024Hardback
9781009426855
677 pages
235 × 159 × 41 mm
1.09kg
Available
Table of Contents
- 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.
