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.

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