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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 ZΑ∞ and the tubes.

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 ZΑ∞ and the tubes.

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 ZΑ∞ and the tubes.