$n$-representation-finite algebras and $n$-APR tilting

Abstract

We introduce the notion of $n$-representation-finiteness, generalizing representation-finite hereditary algebras. We establish the procedure of $n$-APR tilting and show that it preserves $n$-representation-finiteness. We give some combinatorial description of this procedure and use this to completely describe a class of $n$-representation-finite algebras called “type A”.