Basic theory of algebraic groups and Lie algebras / Gerhard P. Hochschild

Auteur: Hochschild, Gerhard Paul (1915-2010) - AuteurType de document: Livre numériqueCollection: Graduate texts in mathematics ; 75Langue: anglaisÉditeur: New York : Springer, 1981 ISBN: 9781461381143 Note: The principal concern of this book is to use the theory of algebraic groups for exhibiting basic algebra (i.e. various basic techniques from field theory, multilinear algebra, commutative ring theory, algebraic geometry and general algebraic representation theory of groups and Lie algebras) in action. Accordingly, the emphasis is made on developing the major general mathematical tools used for gaining control over algebraic groups, rather than on securing the final definitive results, such as the classification of simple groups and their irreducible representations. The exposition is entirely self-contained; no detailed knowledge beyond the usual standard material of the first one or two years graduate study in algebra is presupposed. (Zentralblatt) Sujets MSC: 20G15 Group theory and generalizations -- Linear algebraic groups and related topics -- Linear algebraic groups over arbitrary fields
17B45 Nonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Lie algebras of linear algebraic groups
14L10 Algebraic geometry -- Algebraic groups -- Group varieties
20G05 Group theory and generalizations -- Linear algebraic groups and related topics -- Representation theory
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The principal concern of this book is to use the theory of algebraic groups for exhibiting basic algebra (i.e. various basic techniques from field theory, multilinear algebra, commutative ring theory, algebraic geometry and general algebraic representation theory of groups and Lie algebras) in action. Accordingly, the emphasis is made on developing the major general mathematical tools used for gaining control over algebraic groups, rather than on securing the final definitive results, such as the classification of simple groups and their irreducible representations. The exposition is entirely self-contained; no detailed knowledge beyond the usual standard material of the first one or two years graduate study in algebra is presupposed. (Zentralblatt)

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