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

by Irving Kaplansky

Comment on this title and you could win free books! Synopses & Reviews Table of Contents Comment on this title and you could win free books! ISBN13: 9780226424538 ISBN10: 0226424537 Condition: Standard All Product Details Only 1 left in stock at $11.50!

 

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.

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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.

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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

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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:

1971

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

Lie Algebras and Locally Compact Groups (Chicago Lectures in Mathematics) Used Trade Paper Irving Kaplansky

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Product details 155 pages University of Chicago Press - 2011-09-22 English 9780226424538 Reviews:

"Synopsis" by Ingram, 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.