Lie Algebras and Locally Compact Groups

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.

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.