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|Material Type:||Internet resource|
|Document Type:||Book, Internet Resource|
|All Authors / Contributors:||
J J Duistermaat; Johan A C Kolk
|Description:||viii, 344 p. : ill. ; 24 cm.|
|Contents:||1. Lie Groups and Lie Algebras. Lie Groups and their Lie Algebras. Examples. The Exponential Map. The Exponential Map for a Vector Space. The Tangent Map of Exp. The Product in Logarithmic Coordinates. Dynkin's Formula. Lie's Fundamental Theorems. The Component of the Identity. Lie Subgroups and Homomorphisms. Quotients. Connected Commutative Lie Groups. Simply Connected Lie Groups. Lie's Third Fundamental Theorem in Global Form --
2. Proper Actions. Review. Bochner's Linearization Theorem. Slices. Associated Fiber Bundles. Smooth Functions on the Orbit Space. Orbit Types and Local Action Types. The Stratification by Orbit Types. Principal and Regular Orbits. Blowing Up --
3. Compact Lie Groups. Centralizers. The Adjoint Action.
|Responsibility:||Johannes J. Duistermaat, Johan A.C. Kolk.|
From the reviews: "This one is worth to read and to keep on your shelf! It presents the theory of Lie groups not only in the usual way of Lie algebraic treatment, but also from the global point of