Lie Algebras and Lie Groups: 1964 Lectures given at Harvard University

Jean-Pierre Serre (auth.)9780387550084, 9783540550082, 0387550089, 3540550089

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.

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Table of contents :
Front Matter….Pages I-VII
Front Matter….Pages 1-1
Lie Algebras: Definition and Examples….Pages 2-5
Filtered Groups and Lie Algebras….Pages 6-10
Universal Algebra of a Lie Algebra….Pages 11-17
Free Lie Algebras….Pages 18-30
Nilpotent and Solvable Lie Algebras….Pages 31-43
Semisimple Lie Algebras….Pages 44-55
Representations of $$ mathfrak{s}mathfrak{l}_mathfrak{n} $$ ….Pages 56-62
Front Matter….Pages 63-63
Complete Fields….Pages 64-66
Analytic Functions….Pages 67-75
Analytic Manifolds….Pages 76-101
Analytic Groups….Pages 102-128
Lie Theory….Pages 129-160
Back Matter….Pages 161-172