This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject.In addition to its accessible treatment of the basic theory of Lie groups and Lie algebras, the book is also noteworthy for includinga treatment of the BakerCampbellHausdorff formula and its use in place of the Frobenius theorem to establish deeper results about the relationship between Lie groups and Lie algebrasmotivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of sl(3C)an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebrasa selfcontained construction of the representations of compact groups, independent of Liealgebraic argumentsThe second edition of Lie Groups, Lie Algebras, and Representations contains many substantial improvements and additions, among them an entirely new part devoted to the structure and representation theory of compact Lie groups a complete derivation of the main properties of root systems the construction of finitedimensional representations of semisimple Lie algebras has been elaborated a treatment of universal enveloping algebras,...

Binding: Hardback;449 pages; Publisher: Springer International Publishing AG; Classification: PBF; Weight: 1008 g; Dimensions: 244 x 160 x 28

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