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Higher Nakayama algebras I : Construction

Jasso, Gustavo LU and Külshammer, Julian (2019) In Advances in Mathematics 351. p.1139-1200
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.
Please use this url to cite or link to this publication:
author
and
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Auslander–Reiten theory, Auslander–Reiten quiver, Nakayama algebras, Cluster-tilting, Homological embedding
in
Advances in Mathematics
volume
351
pages
62 pages
publisher
Academic Press
external identifiers
  • scopus:85066485799
ISSN
0001-8708
DOI
10.1016/j.aim.2019.05.026
language
English
LU publication?
no
additional info
With an appendix by Julian Külshammer and Chrysostomos Psaroudakis and an appendix by Sondre Kvamme.
id
198ef02b-0db4-4398-a370-b23e6acb9b38
date added to LUP
2022-03-09 15:04:33
date last changed
2025-10-14 13:20:42
@article{198ef02b-0db4-4398-a370-b23e6acb9b38,
  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.}},
  author       = {{Jasso, Gustavo and Külshammer, Julian}},
  issn         = {{0001-8708}},
  keywords     = {{Auslander–Reiten theory; Auslander–Reiten quiver; Nakayama algebras; Cluster-tilting; Homological embedding}},
  language     = {{eng}},
  pages        = {{1139--1200}},
  publisher    = {{Academic Press}},
  series       = {{Advances in Mathematics}},
  title        = {{Higher Nakayama algebras I : Construction}},
  url          = {{http://dx.doi.org/10.1016/j.aim.2019.05.026}},
  doi          = {{10.1016/j.aim.2019.05.026}},
  volume       = {{351}},
  year         = {{2019}},
}