I work on cluster algebras and quivers and hence I need to understand Auslander-Reiten theory and tilting theory as soon as possible. I have read some noncommutative algebra and homological algebra but still have trouble pondering on Auslander-Reiten-Smalo's book, Representation Theory of Artin Algebras. Without Auslander-Reiten theory I can not understand tilting theory, either. May I ask what shall I learn in order to understand both of them? Thank you very much!
2026-04-01 23:12:01.1775085121
What shall I learn in order to understand Auslander-Reiten theory and tilting theory?
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I'd recommend the book Elements of the Representation Theorey of Associative Algebras by Assem, Simson, & Skowroński. It covers both Auslander-Rieten Theory, Tilting Theory, and almost all of the background required to understand those chapters.