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 -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_infinity and the tubes.
Bibliografisk informationWith an appendix by Julian Külshammer and Chrysostomos Psaroudakis and an appendix by Sondre Kvamme.
- Algebra och logik