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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 motivation and intuition for proofs is provided than in most classic texts on the subjectIn 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 algebrasmotivation for the machinery of roots, weights and the Weyl group via a concrete and detailed exposition of the representation theory of slC an unconventional definition of semisimplicity that allows for a rapid development of the structure theory of semisimple Lie algebrasa self contained construction of the representations of compact groups, independent of Lie algebraic 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 finite dimensional representations of semisimple Lie algebras has been elaborated a treatment of universal enveloping algebras, including a proof of the Poincar Birkhoff Witt theorem and the existence of Verma modules complete proofs of the Weyl character formula, the Weyl dimension formula and the Kostant multiplicity formulaReview 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

14 thoughts on “Lie Groups, Lie Algebras, and Representations: An Elementary Introduction (Graduate Texts in Mathematics)

  1. Adriano Adriano says:

    It s been a long time since I didn t receive a decent printed book with the old standards from Springer I usually don t complain about the intellectual parts of the books I bought Springer, in that respect, has always had very high standards rather, I complain about the change in printing qualities of the so called print on demand books Specially because they are not cheaper than their counter parts that where printed decently They ought to cost a tenth of their real price in order not to feel robbed for what you receive.Curiously, it seams that this book was printed in Switzerland, so I presume that their politics hasn t change such as in the United States of North America and Mexico, where the printing qualities are terrible these days and the books are really expensive for the trash one receives So I would advise stop buying them unless we know where they where printed.

  2. Cliente de Cliente de says:

    For a general introduction it s a great book, in particular the matrcula form of the Lie groups and algebras makes the concepts easier to handle The author has nice well to give hard concepts in an easy way.

  3. PlasmaStorm PlasmaStorm says:

    pieno anche di esempi, che aiutano a meglio farsi un idea della fondamentale algebra di Lie Un approccio matematico ma orientato comunque all uso in fisica.

  4. Customer Customer says:

    Great book

  5. Hua Wang Hua Wang says:

    I love this book

  6. Brian Beckman Brian Beckman says:

    Brian Hall has written the best book I know and I have several on this challenging topic The concepts are easy, but the number of different kinds of things one needs to remember to master this topic, to apply it, and to do calculations with it is large Hall takes the time to spell out the structure and relationships that make remembering the zoo much easier, at least for me If you re inclined to remember things by their structure and relationships as opposed to their mere taxonomy , then you will get a lot out of this book.

  7. Batuhan BAYIR Batuhan BAYIR says:

    This book is very well introduction to this topic because have a minimal prerequisites For example Part 1 using only Linear algebra Further, in Part 1 Hall explains matrix Lie groups with many examples and some geometrical physical interpretations I recommend this book for both mathematicians and physicists.

  8. William Varenas William Varenas says:

    Great book and service

  9. Customer Customer says:

    Great book

  10. A graduate student A graduate student says:


  11. AlunWyn-jones AlunWyn-jones says:

    This was perfect for what I wanted I am reacquainting myself with some concepts and learning a lot of new stuff too.

  12. Raybrown Raybrown says:


  13. Lucian Petris Lucian Petris says:

    Not very user friendly if not up to this level of group theory.

  14. mengda lei mengda lei says: