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

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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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.
Content:
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

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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.
Content:
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
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