Introduction to Lie Algebras

by Karin Erdmann, Mark J. Wildon

Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right. This book provides an elementary introduction to Lie algebras based on a lecture course given to fourth-year undergraduates. The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality. Numerous worked examples and exercises are provided to test understanding, along with more demanding problems, several of which have solutions. Introduction to Lie Algebras covers the core material required for almost all other work in Lie theory and provides a self-study guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics.

Genres: Mathematics, Algebra, Lie

263 pages, Paperback

First published April 4, 2006

Reviews

[Erickson · Rating 4 out of 5]

I think this book is well-written for first few chapters: it gives gentle introduction to Lie algebra really well and suitable for undergraduates. For latter chapters, there are many "jumps" which may be at times messy and need quite a lot of efforts to fill, and quite nontrivial ones. Choice of phrasing is also at times a bit confusing (e.g. acts diagonalizably). And also the huge amount of errata. On one hand it is alright if one has huge mastery of linear algebra, but otherwise a modest amount of knowledge in linear algebra sometimes isn't enough. But overall, it does allow undergraduates to taste Lie algebra quite early.