τ2-stable tilting complexes over weighted projective lines
(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:
https://lup.lub.lu.se/record/83f264b1-f693-4d17-af01-c03e917af78a
- author
- Jasso, Gustavo LU
- publishing date
- 2015-03
- 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}}, }