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

Forskningsoutput: Tidskriftsbidrag › Artikel i vetenskaplig tidskrift › Peer review

Sammanfattning

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.

Originalspråk	engelska
Sidor (från-till)	1139-1200
Antal sidor	62
Tidskrift	Advances in Mathematics
Volym	351
DOI	https://doi.org/10.1016/j.aim.2019.05.026
Status	Published - 2019
Externt publicerad	Ja

Bibliografisk information

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

Ämnesklassifikation (UKÄ)

Algebra och logik

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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 = "Elsevier",

}

TY - JOUR

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

Sammanfattning

Bibliografisk information

Ämnesklassifikation (UKÄ)

Tillgång till dokument

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