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arXiv · 1604.03500

Higher Nakayama algebras I: Construction

Gustavo Jasso·Julian Külshammer
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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 $\mathbb{ZA}_\infty$ and the tubes.

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BibTeXRIS

Gustavo Jasso, Julian Külshammer. 2016-04-12. Higher Nakayama algebras I: Construction. https://doi.org/10.1016/j.aim.2019.05.026

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