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An introduction to higher Auslander-Reiten theory

Jasso, Gustavo LU and Kvamme, Sondre (2019) In Bulletin of the London Mathematical Society 51(1). p.1-24
Abstract
This article consists of an introduction to Iyama's higher Auslander–Reiten theory for Artin algebras from the viewpoint of higher homological algebra. We provide alternative proofs of the basic results in higher Auslander–Reiten theory, including the existence of d-almost-split sequences in d-cluster-tilting subcategories, following the approach to classical Auslander–Reiten theory due to Auslander, Reiten, and Smalø. We show that Krause's proof of Auslander's defect formula can be adapted to give a new proof of the defect formula for d-exact sequences. We use the defect formula to establish the existence of morphisms determined by objects in d-cluster-tilting subcategories.
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author
and
publishing date
type
Contribution to journal
publication status
published
subject
in
Bulletin of the London Mathematical Society
volume
51
issue
1
pages
24 pages
publisher
Oxford University Press
external identifiers
  • scopus:85053938429
ISSN
0024-6093
DOI
10.1112/blms.12204
language
English
LU publication?
no
id
95425013-e5bb-402b-a223-dbdb21a4000a
date added to LUP
2022-03-09 15:07:11
date last changed
2022-04-26 00:26:33
@article{95425013-e5bb-402b-a223-dbdb21a4000a,
  abstract     = {{This article consists of an introduction to Iyama's higher Auslander–Reiten theory for Artin algebras from the viewpoint of higher homological algebra. We provide alternative proofs of the basic results in higher Auslander–Reiten theory, including the existence of d-almost-split sequences in d-cluster-tilting subcategories, following the approach to classical Auslander–Reiten theory due to Auslander, Reiten, and Smalø. We show that Krause's proof of Auslander's defect formula can be adapted to give a new proof of the defect formula for d-exact sequences. We use the defect formula to establish the existence of morphisms determined by objects in d-cluster-tilting subcategories.}},
  author       = {{Jasso, Gustavo and Kvamme, Sondre}},
  issn         = {{0024-6093}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{1--24}},
  publisher    = {{Oxford University Press}},
  series       = {{Bulletin of the London Mathematical Society}},
  title        = {{An introduction to higher Auslander-Reiten theory}},
  url          = {{http://dx.doi.org/10.1112/blms.12204}},
  doi          = {{10.1112/blms.12204}},
  volume       = {{51}},
  year         = {{2019}},
}