Higher Nakayama algebras I: Construction

By Gustavo Jasso, Julian Kulshammer. Advances in Mathematics, 2016

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Abstract 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

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