Albert Algebras over Commutative Rings

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 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 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.

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.