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Lie Algebras and Locally Compact Groups : Chicago Lectures in Mathematics - Irving Kaplansky

Lie Algebras and Locally Compact Groups

Chicago Lectures in Mathematics

Paperback

Published: 1st January 1971
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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.

Preface
Lie Algebras
Definitions and examples
Solvable and nilpotent algebras
Semi-simple algebras
Cartan subalgebras
Transition to a geometric problem (characteristic 0)
The geometric classification
Transition to a geometric problem (characteristicnbsp; p)
Transition to a geometric problem (characteristic p), continued
The Structure of Locally Compact Groups
NSS groups
Existence of one-parameter subgroups
Differentiablenbsp; functions
Functions constructed from a single Q
Functions constructed from a sequence of Q's
Proof that i/n. is bounded
Existence of proper differentiable functions
The vector space of one-parameter subgroups
Proof that K is a neighborhood of 1
Approximation by NSS groups
Further developments
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780226424538
ISBN-10: 0226424537
Series: Chicago Lectures in Mathematics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 160
Published: 1st January 1971
Publisher: The University of Chicago Press
Country of Publication: US
Dimensions (cm): 20.32 x 13.97  x 1.27
Weight (kg): 0.18