Higher Nakayama algebras I: Construction.

We introduce higher dimensional analogues of the Nakayama algebras from the viewpoint of Iyama's higher Auslander–Reiten theory. More precisely, for each Nakayama algebra A and each positive integer d , we construct a finite dimensional algebra A (d) having a distinguished d -cluster-tilting A (d) -module whose endomorphism algebra is a higher dimensional analogue of the Auslander algebra of A. We also construct higher dimensional analogues of the mesh category of type ZA ∞ and the tubes. [ABSTRACT FROM AUTHOR]