Albert Algebras over Commutative Rings

The Last Frontier of Jordan Systems

Series:

Author:

Skip Garibaldi, Institute for Defense Analyses, USA
Holger P. Petersson, FernUniversität in Hagen
Michel L. Racine, University of Ottawa

Published:

No date available

Format:

Hardback

ISBN:

9781009426855

Hardback

Description

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.

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

Published: No date available
Format: Hardback
ISBN: 9781009426855
Length: 677 pages
Dimensions: 235 × 159 × 41 mm
Weight: 1.09kg

Often bought together

This title is available for institutional purchase via Cambridge Core

Learn more

Related Journals

Also by this Author

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.

Look inside

Courses

Resources

Displaying 1 - 1 of 1

Solutions to exercises

Follow link

Additional Information

About the authors

Authors

Skip Garibaldi , Institute for Defense Analyses, USA
Skip Garibaldi is Director of the IDA Center for Communications Research, La Jolla. His research focuses on algebraic groups, especially exceptional groups, which naturally involves studying Albert algebras. He is co-author of the book 'Cohomological Invariants in Galois Cohomology (2003),' written with Alexander Merkurjev and Jean-Pierre Serre. He is a Fellow of the American Mathematical Society and received the Lester R. Ford Award from the Mathematical Association of America.
Holger P. Petersson , FernUniversität in Hagen
Holger P. Petersson is Emeritus Professor in the Faculty of Mathematics and Computer Science at FernUniversität in Hagen, Germany. He has published on non-associative algebras, especially Albert algebras, over the course of his whole career, and is the author of a key survey on Albert algebras over fields of arbitrary characteristic, which was a starting point for this book. He co-wrote the monograph 'Descent in Buildings' with Bernhard Mühlherr and Richard Weiss.
Michel L. Racine , University of Ottawa
Michel L. Racine is Emeritus Professor in the Department of Mathematics and Statistics at the University of Ottawa. His research interests include Jordan algebras and superalgebras, especially Albert algebras. He has proved many key results in this book, either alone or in joint work with Petersson. He was a von Humboldt Fellow at Universität Münster and an SSHN Fellow at Université Paris 5.

Products and services

About us