Albert Algebras over Commutative Rings - Garibaldi, Skip; Petersson, Holger P.; Racine, Michel L.
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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,…mehr

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Produktbeschreibung
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.
Autorenporträt
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.