n-representation-finite algebras and n-APR tilting

TL;DR

This paper introduces n-representation-finiteness as a generalization of classical finiteness in hereditary algebras, develops n-APR tilting, and characterizes a class of such algebras called 'type A' using combinatorial methods.

Contribution

It defines n-representation-finiteness, develops the n-APR tilting procedure, and provides a combinatorial classification of type A n-representation-finite algebras.

Findings

n-representation-finiteness generalizes classical representation-finiteness.

n-APR tilting preserves n-representation-finiteness.

Complete combinatorial description of type A n-representation-finite algebras.

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".