Higher Nakayama algebras I: Construction

Gustavo Jasso; Julian Külshammer

doi:10.1016/j.aim.2019.05.026

Higher Nakayama algebras I: Construction

Gustavo Jasso, Julian Külshammer

Research output: Contribution to journal › Article › peer-review

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 -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.

Original language	English
Pages (from-to)	1139-1200
Number of pages	62
Journal	Advances in Mathematics
Volume	351
DOIs	https://doi.org/10.1016/j.aim.2019.05.026
Publication status	Published - 2019
Externally published	Yes

Bibliographical note

With an appendix by Julian Külshammer and Chrysostomos Psaroudakis and an appendix by Sondre Kvamme.

Subject classification (UKÄ)

Algebra and Logic

Free keywords

Auslander–Reiten theory
Auslander–Reiten quiver
Nakayama algebras
Cluster-tilting
Homological embedding

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10.1016/j.aim.2019.05.026

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title = "Higher Nakayama algebras I: Construction",

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 -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.",

keywords = "Auslander–Reiten theory, Auslander–Reiten quiver, Nakayama algebras, Cluster-tilting, Homological embedding",

author = "Gustavo Jasso and Julian K{\"u}lshammer",

note = "With an appendix by Julian K{\"u}lshammer and Chrysostomos Psaroudakis and an appendix by Sondre Kvamme.",

year = "2019",

doi = "10.1016/j.aim.2019.05.026",

language = "English",

volume = "351",

pages = "1139--1200",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press",

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T1 - Higher Nakayama algebras I

T2 - Construction

AU - Jasso, Gustavo

AU - Külshammer, Julian

N1 - With an appendix by Julian Külshammer and Chrysostomos Psaroudakis and an appendix by Sondre Kvamme.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Auslander–Reiten theory

KW - Auslander–Reiten quiver

KW - Nakayama algebras

KW - Cluster-tilting

KW - Homological embedding

U2 - 10.1016/j.aim.2019.05.026

DO - 10.1016/j.aim.2019.05.026

M3 - Article

SN - 0001-8708

VL - 351

SP - 1139

EP - 1200

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Higher Nakayama algebras I: Construction

Abstract

Bibliographical note

Subject classification (UKÄ)

Free keywords

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Cite this