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Nakayama-type phenomena in higher Auslander-Reiten theory

Jasso, Gustavo LU and Külshammer, Julian (2018) In Contemporary Mathematics 705. p.79-98
Abstract
This paper surveys recent contructions in higher Auslander–Reiten theory. We focus on those which, due to their combinatorial properties, can be regarded as higher dimensional analogues of path algebras of linearly oriented type A quivers. These include higher dimensional analogues of Nakayama algebras, of the mesh category of type ZA∞ and the tubes, and of the triangulated category generated by an m-spherical object. For m = 2, the latter category can be regarded as the higher cluster category of type A∞ whose cluster-tilting combinatorics are controlled by the triangulations of the cylic apeirotope.
Please use this url to cite or link to this publication:
author
and
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
Representations of algebras
series title
Contemporary Mathematics
volume
705
pages
20 pages
publisher
American Mathematical Society (AMS)
external identifiers
  • scopus:85050021009
ISSN
0271-4132
1098-3627
ISBN
978-1-4704-3576-9
978-1-4704-4721-2
DOI
10.1090/conm/705/14191
language
English
LU publication?
no
id
624cb59d-600e-4b4f-aa56-29f6d950d91f
date added to LUP
2022-03-09 15:47:54
date last changed
2025-07-12 00:25:48
@inbook{624cb59d-600e-4b4f-aa56-29f6d950d91f,
  abstract     = {{This paper surveys recent contructions in higher Auslander–Reiten theory. We focus on those which, due to their combinatorial properties, can be regarded as higher dimensional analogues of path algebras of linearly oriented type A quivers. These include higher dimensional analogues of Nakayama algebras, of the mesh category of type ZA∞ and the tubes, and of the triangulated category generated by an m-spherical object. For m = 2, the latter category can be regarded as the higher cluster category of type A∞ whose cluster-tilting combinatorics are controlled by the triangulations of the cylic apeirotope.}},
  author       = {{Jasso, Gustavo and Külshammer, Julian}},
  booktitle    = {{Representations of algebras}},
  isbn         = {{978-1-4704-3576-9}},
  issn         = {{0271-4132}},
  language     = {{eng}},
  pages        = {{79--98}},
  publisher    = {{American Mathematical Society (AMS)}},
  series       = {{Contemporary Mathematics}},
  title        = {{Nakayama-type phenomena in higher Auslander-Reiten theory}},
  url          = {{http://dx.doi.org/10.1090/conm/705/14191}},
  doi          = {{10.1090/conm/705/14191}},
  volume       = {{705}},
  year         = {{2018}},
}