Lie Algebras and Lie Groups: 1964 Lectures given at Harvard University (Lecture Notes in Mathematics) (Paperback)

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Key Phrases: analytic group homomorphism, group submanifold, ultrametric field, George Bergman (more...)

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Product Description

This book reproduces J-P. Serre's 1964 Harvard lectures. The aim is to introduce the reader to the "Lie dictionary": Lie algebras and Lie groups. Special features of the presentation are its emphasis on formal groups (in the Lie group part) and the use of analytic manifolds on p-adic fields. Some knowledge of algebra and calculus is required of the reader, but the text is easily accessible to graduate students, and to mathematicians at large.

Product Details

• Paperback: 168 pages
• Publisher: Springer; 2nd edition (October 18, 2005)
• Language: English
• ISBN-10: 3540550089
• ISBN-13: 978-3540550082
• Product Dimensions: 9.2 x 6.1 x 0.4 inches
• Shipping Weight: 9.6 ounces (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon.com Sales Rank: #698,357 in Books (See Bestsellers in Books)

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10 of 10 people found the following review helpful:

4.0 out of 5 stars Nice and complete, but very Bourbaki-looking., May 4, 2000

By	Bernardo Vargas (Weimar, Germany) - See all my reviews

This review is from: Lie Algebras and Lie Groups: 1964 Lectures Given at Harvard University (Grundlehren Der Mathematischen Wissenschaften) (Paperback)

The same problem with all Bourbaki authors: They treat the subject in a very concise, abstract, and authoritative way, but present almost no motivation to introduce the subject, and they are not so used to give extensive and accurate references. Of course Serre is a leading expert in the field, but he (nobody) cannot be regarded as the inventor of the theory, so the absence of such a bibliography is not justifiable.

The contents of the book are: Lie algebras, filtered groups and lie algebras, universal algebra of a Lie algebra, free Lie algebras, nilpotent and solvable Lie algebras, semisimple Lie algebras, representations of sl_n, complete fields, analytic functions, analytic manifolds, analytic groups, Lie theory. Includes excercises.

Useful for graduate students and working mathematicians, along with a "lighter" reference.

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