Resources

This book by Humphreys was my introduction to Lie algebras and their representation theory. It is also quite popular in the community of representation theorists whose work even remotely pertains to Lie algebras. What more can I say besides give it a chance? You will not be disappointed.

This second book by Humphreys is also a great read. I only started reading it near the beginning of August of 2020, but I wish I had read it concurrently with the other book. This book is very thorough and hence, cited quite often even decades after its publication.

This book by Carter was my introduction to Kac-Moody algebras. Well, my first intro was actually through a book by Kac, but it was rather difficult to read and had an awkward pacing. Thankfully, Carter’s book is very concise and presents all of the details in a comfortable pace and logical order. Since reading through it, there are certainly other nice treatments of Affine Lie algebras, but Carter’s book will always be a staple in my library.

This book by Jantzen was my introduction to Quantum Groups, or rather Quantized Universal Enveloping Algebras. His proofs are very clear and the logic is natural, which I found especially encouraging since this was my first exposure to the topic. Others like Kassel, Chari and Pressley, and Lusztig come to mind wen thinking of Quantum Groups. However, Janzten’s treatment is certainly more to the point.

This book by Hong and Kang is an excellent book if you already have some familiarity with Quantum Groups with a fair background in Lie algebras and Kac-Moody algebras, and are now interested in studying Crystal Bases.

This book by Etingof et. al. is a remarkably concise and direct presentation of tensor categories. Keep in mind that the terminology in the book is not necessarily ubiquitous in the community or standard e.g. you should be cautious by what an author means by tensor category, they might just mean monoidal!

This book by Turaev is an excellent book for a couple of reasons. I happened upon it because I was interested in how Quantum Groups led to (quantum) knot invariants. This book tackles this topic and far more than I expected. It is what I am currently reading as of the Fall semester of 2020.

This book by Aluffi is a remarkable book that my first professor in undergraduate algebra used. It was then also my first introduction to category theory because Aluffi presents many of the rather typical definitions of, say, group theory with some categorical motivation. Perhaps my professor at the time was ambitious to use it for a first semester of algebra, but hey, no complaints here!

This book by Bosch was a nice introduction to commutative algebra and some of the methods in Homological algebra. I tend to refer to it for some of the theorems since his proofs are either complete and concise, or at least clear enough that the reader should feel confident in filling in the missing pieces.

This book by Folland on Real Analysis is absolutely a great resource. The author is surprisingly clear and presents all proofs with such clarity. I am certainly more of a fan on algebra and abstract structures, but this book honestly gave me a new appreciation for analysis.