Introduction to Lie Algebras (Springer Undergraduate Mathematics Series) by K. Erdmann (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐With very nice (and not at all always easy) exercises. Requires hardly any background (linear algebra is, not surprisingly, essential; group theory very helpful). MUCH better for a beginner than the Bourbakist treatments.

⭐As a senior math major I decided I wished to learn Lie Algebra, and based on my experience with the SUMS Number Theory book, I chose this one. I am taking a reading course on Lie Algebras which consists of me reading and doing the problems and asked the teacher if i have issues. This book is perfect. In about two weeks I have gotten through the first 11 chapters, and done about 80% of the problems. In addition to being very clear and simple, it is very complete. Often my adviser will ask if the book covered a particular concept, it has yet to fail. It also provides some nice examples to relate to. Unfortunately it does have several typos and not a complete solution guide, these things kept it from the 5. I especially recommend this book for self-study.

⭐I am an amateur cosmologist and wanted to try my hand with Lie Algebras. Alas, this was not really the book for me. I was disappointed to find no glossary (ended up writing my own), hence the book was difficult to read. The authors have a habit of using “critical exercises” (sometimes without proof in the appendix) as the essence of the next steps. The good news is that I now do have an understanding of Lie Algebras, but not without reference to the Wiki Maths to complement the book.

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