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Claude Chevalley - Theory of Lie Groups (PMS-8), Volume 8 - 9780691049908 - V9780691049908
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Theory of Lie Groups (PMS-8), Volume 8

€ 123.30
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Description for Theory of Lie Groups (PMS-8), Volume 8 Paperback. A treatise on Lie groups in which a modern point of view was adopted systematically, namely, that a continuous group can be regarded as a global object. This book incorporates a broad range of topics, such as the covering spaces of topological spaces, analytic manifolds, and integration of complete systems of differential equations on a manifold. Series: Princeton Mathematical Series. Num Pages: 232 pages, Ill. BIC Classification: PBF; PBG. Category: (P) Professional & Vocational; (U) Tertiary Education (US: College). Dimension: 229 x 152 x 14. Weight in Grams: 314.
This famous book was the first treatise on Lie groups in which a modern point of view was adopted systematically, namely, that a continuous group can be regarded as a global object. To develop this idea to its fullest extent, Chevalley incorporated a broad range of topics, such as the covering spaces of topological spaces, analytic manifolds, integration of complete systems of differential equations on a manifold, and the calculus of exterior differential forms. The book opens with a short description of the classical groups: unitary groups, orthogonal groups, symplectic groups, etc. These special groups are then used to illustrate the general properties of Lie groups, which are considered later. The general notion of a Lie group is defined and correlated with the algebraic notion of a Lie algebra; the subgroups, factor groups, and homomorphisms of Lie groups are studied by making use of the Lie algebra. The last chapter is concerned with the theory of compact groups, culminating in Peter-Weyl's theorem on the existence of representations. Given a compact group, it is shown how one can construct algebraically the corresponding Lie group with complex parameters which appears in the form of a certain algebraic variety (associated algebraic group). This construction is intimately related to the proof of the generalization given by Tannaka of Pontrjagin's duality theorem for Abelian groups. The continued importance of Lie groups in mathematics and theoretical physics make this an indispensable volume for researchers in both fields.

Product Details

Format
Paperback
Publication date
2000
Publisher
Princeton University Press United States
Number of pages
232
Condition
New
Series
Princeton Mathematical Series
Number of Pages
232
Place of Publication
New Jersey, United States
ISBN
9780691049908
SKU
V9780691049908
Shipping Time
Usually ships in 7 to 11 working days
Ref
99-1

About Claude Chevalley
Claude Chevalley (1909-1984) served on the faculty of Princeton University and was resident at the Institute for Advanced Study. He was a member of the Bourbaki and was awarded the Cole Prize of the American Mathematical Society.

Reviews for Theory of Lie Groups (PMS-8), Volume 8
"Chevalley's most important contribution to mathematics is certainly his work on group theory ... [Theory of Lie Groups] was the first systematic exposition of the foundations of Lie group theory consistently adopting the global viewpoint, based on the notion of analytic manifold. This book remained the basic reference on Lie groups for at least two decades."
Bulletin of the American Mathematical Society

Goodreads reviews for Theory of Lie Groups (PMS-8), Volume 8


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