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τ2-stable tilting complexes over weighted projective lines

Jasso, Gustavo LU (2015) In Advances in Mathematics 273. p.1-31
Abstract
Let X be a weighted projective line and coh X the associated category of coherent sheaves. We classify the tilting complexes T in Db(coh X) such that τ2T ≅ T , where τ is the Auslander–Reiten translation in Db(coh X). As an application of this result, we classify the 2-representation-finite algebras which are derived-equivalent to a canonical algebra. This complements Iyama-Oppermann’s classification of the iterated tilted 2-representation-finite algebras. By passing to 3-preprojective algebras, we obtain a classification of the selfinjective cluster-tilted algebras of canonical-type. This complements Ringel’s classification of the selfinjective cluster-tilted algebras.
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
in
Advances in Mathematics
volume
273
pages
31 pages
publisher
Elsevier
external identifiers
  • scopus:84921501247
ISSN
0001-8708
DOI
10.1016/j.aim.2014.12.018
language
English
LU publication?
no
id
83f264b1-f693-4d17-af01-c03e917af78a
date added to LUP
2022-03-09 15:18:48
date last changed
2023-03-08 09:35:03
@article{83f264b1-f693-4d17-af01-c03e917af78a,
  abstract     = {{Let X be a weighted projective line and coh X the associated category of coherent sheaves. We classify the tilting complexes T in D<sup>b</sup>(coh X) such that τ<sup>2</sup>T ≅ T , where τ is the Auslander–Reiten translation in D<sup>b</sup>(coh X). As an application of this result, we classify the 2-representation-finite algebras which are derived-equivalent to a canonical algebra. This complements Iyama-Oppermann’s classification of the iterated tilted 2-representation-finite algebras. By passing to 3-preprojective algebras, we obtain a classification of the selfinjective cluster-tilted algebras of canonical-type. This complements Ringel’s classification of the selfinjective cluster-tilted algebras.}},
  author       = {{Jasso, Gustavo}},
  issn         = {{0001-8708}},
  language     = {{eng}},
  pages        = {{1--31}},
  publisher    = {{Elsevier}},
  series       = {{Advances in Mathematics}},
  title        = {{τ<sup>2</sup>-stable tilting complexes over weighted projective lines}},
  url          = {{http://dx.doi.org/10.1016/j.aim.2014.12.018}},
  doi          = {{10.1016/j.aim.2014.12.018}},
  volume       = {{273}},
  year         = {{2015}},
}