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Lie Algebras and Locally Compact Groups (Chicago Lectures in Mathematics)

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Lie Algebras and Locally Compact Groups (Chicago Lectures in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

This volume presents lecture notes based on the author's courses on Lie algebras and the solution of Hilbert's fifth problem. In chapter 1, "Lie Algebras," the structure theory of semi-simple Lie algebras in characteristic zero is presented, following the ideas of Killing and Cartan. Chapter 2, "The Structure of Locally Compact Groups," deals with the solution of Hilbert's fifth problem given by Gleason, Montgomery, and Zipplin in 1952.

Synopsis:

This volume-brought back into print because of the continued importance of the mathematics involved-makes available Irving Kaplansky's classic lecture notes from his courses on Lie algebras and the solution of Hilbert's fifth problem.

About the Author

Irving Kaplansky is Director Emeritus of the Mathematical Sciences Research Institute and George Herbert Mead Distinguished Professor Emeritus in the Department of Mathematics at the University of Chicago.

Table of Contents

PREFACE

Chapter I. LIE ALGEBRAS

1. Definitions and examples

2. Solvable and nilpotent algebras

3. Semi-simple algebras

4. Cartan subalgebras

5. Transition to a geometric problem

(characteristic 0)

6. The geometric classification

7. Transition to a geometric problem

(characteristic  p)

8. Transition to a geometric problem

(characteristic p), continued

Chapter II. THE STRUCTURE OF LOCALLY COMPACT GROUPS

1. NSS groups

2. Existence of one-parameter subgroups

3.  Differentiable  functions

4. Functions constructed from a single Q

5. Functions constructed from a sequence of Q's

6. Proof that i/n. is bounded

7. Existence of proper differentiable functions

8. The vector space of one-parameter subgroups

9. Proof that K is a neighborhood of 1

10. Approximation by NSS groups

11. Further developments

BIBLIOGRAPHY

INDEX

Product Details

ISBN:
9780226424538
Author:
Kaplansky, Irving
Publisher:
University of Chicago Press
Location:
Chicago
Subject:
Topology
Subject:
Lie groups
Subject:
Lie algebras
Subject:
Locally compact groups.
Subject:
Topology - General
Subject:
MATHEMATICS / Topology
Copyright:
Edition Description:
Paperback
Series:
Chicago Lectures in Mathematics (Paperback)
Series Volume:
v. 21
Publication Date:
19950231
Binding:
TRADE PAPER
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
Yes
Pages:
155
Dimensions:
8 x 5.25 in

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Related Subjects

Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Algebra » Lie Groups and Algebra
Science and Mathematics » Mathematics » Group Theory
Science and Mathematics » Mathematics » Topology

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Product details 155 pages University of Chicago Press - English 9780226424538 Reviews:
"Synopsis" by , This volume-brought back into print because of the continued importance of the mathematics involved-makes available Irving Kaplansky's classic lecture notes from his courses on Lie algebras and the solution of Hilbert's fifth problem.
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