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 $\mathbb{ZA}_\infty$ and the tubes.
Comment: v5: 50 pages, further minor corrections following referee report. With an appendix by the second named author and Chrysostomos Psaroudakis and an appendix by Sondre Kvamme