Claude Chevalley

(Author)

Theory of Lie GroupsPaperback, 10 January 2000

Theory of Lie Groups
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Part of Series
Princeton Mathematical
Part of Series
Princeton Landmarks in Mathematics and Physics
Part of Series
Princeton Landmarks in Mathematics
Print Length
232 pages
Language
English
Publisher
Princeton University Press
Date Published
10 Jan 2000
ISBN-10
0691049904
ISBN-13
9780691049908

Description

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

Author:
Claude Chevalley
Book Format:
Paperback
Country of Origin:
US
Date Published:
10 January 2000
Dimensions:
22.83 x 15.19 x 1.45 cm
ISBN-10:
0691049904
ISBN-13:
9780691049908
Language:
English
Location:
Princeton
Pages:
232
Weight:
272.16 gm

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