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Books > Science & Mathematics > Mathematics > Geometry > Analytic geometry
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Lie Groups, Lie Algebras, and Representations - An Elementary Introduction (Hardcover, 2nd ed. 2015, Corr. 2nd printing 2016)
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Lie Groups, Lie Algebras, and Representations - An Elementary Introduction (Hardcover, 2nd ed. 2015, Corr. 2nd printing 2016)
Series: Graduate Texts in Mathematics, 222
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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 including: a treatment of
the Baker-Campbell-Hausdorff formula and its use in place of the
Frobenius theorem to establish deeper results about the
relationship between Lie groups and Lie algebras motivation for the
machinery of roots, weights and the Weyl group via a concrete and
detailed exposition of the representation theory of sl(3;C) an
unconventional definition of semisimplicity that allows for a rapid
development of the structure theory of semisimple Lie algebras a
self-contained construction of the representations of compact
groups, independent of Lie-algebraic arguments The 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 finite-dimensional representations of
semisimple Lie algebras has been elaborated; a treatment of
universal enveloping algebras, including a proof of the
Poincare-Birkhoff-Witt theorem and the existence of Verma modules;
complete proofs of the Weyl character formula, the Weyl dimension
formula and the Kostant multiplicity formula. Review of the first
edition: This is an excellent book. It deserves to, and undoubtedly
will, become the standard text for early graduate courses in Lie
group theory ... an important addition to the textbook literature
... it is highly recommended. - The Mathematical Gazette
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