HCM: Introduction to Lie algebrasSkip to main content Skip to table of contents. Advertisement Hide. Introduction to Lie Algebras and Representation Theory. Front Matter Pages i-xiii. Basic Concepts.
Introduction to Lie Algebras and Representation Theory
Corrections: There is now as of October a corrected second printing of the second edition, available from Amazon. The second printing fixes many typos in the first printing and also clarifies a few proofs in Chapter 9. If the acknowledgments section at the end of the preface mentions "additional input on the second printing of the second edition," you have the corrected second printing. Here is a list of errata to the first printing of the second edition: erratum2. These have been corrected in the second printing. Here is a revised version of Section 9. This has been incorporated into the second printing.
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Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces , and studies modules over these abstract algebraic structures. The algebraic objects amenable to such a description include groups , associative algebras and Lie algebras. The most prominent of these and historically the first is the representation theory of groups , in which elements of a group are represented by invertible matrices in such a way that the group operation is matrix multiplication. Representation theory is a useful method because it reduces problems in abstract algebra to problems in linear algebra , a subject that is well understood. Representation theory is pervasive across fields of mathematics, for two reasons. First, the applications of representation theory are diverse:  in addition to its impact on algebra, representation theory:. Secondly, there are diverse approaches to representation theory.
This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on Introduction to Lie Algebras and Representation Theory Download book PDF.
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