Higher-dimensional Auslander–Reiten theory on maximal orthogonal subcategories

Abstract

We introduce the concept of maximal ( n − 1 ) -orthogonal subcategories over Artin algebras and orders, and develop ( n + 1 ) -dimensional Auslander–Reiten theory on them. We give the n-Auslander–Reiten translation and the n-Auslander–Reiten duality, then show the existence of n-almost split sequences and n-fundamental sequences. We give some examples.