Lie Algebras and Locally Compact Groups

by Irving Kaplansky

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.

Genres: Mathematics

155 pages, Paperback

First published February 27, 1995

Reviews

[Manny · Rating 4 out of 5]

Not everyone knows that "Lie" is correctly pronounced "Lee-eh" when it refers to a group or algebra. And it's also rather extraordinary that the structure of Lie algebras was largely worked out by someone called Killing. You couldn't make this up.

The book does a great job of explaining Killing and Cartan's analysis, which is renowned among algebraists for its extreme and unexpected beauty. One of those cases where you solve a problem by transforming it into a completely different one.