Roots of Nakayama and Auslander-Reiten translations

Helmut Lenzing; Andrzej Skowroński

Colloquium Mathematicae (2000)

  • Volume: 86, Issue: 2, page 209-230
  • ISSN: 0010-1354

Abstract

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We discuss the roots of the Nakayama and Auslander-Reiten translations in the derived category of coherent sheaves over a weighted projective line. As an application we derive some new results on the structure of selfinjective algebras of canonical type.

How to cite

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Lenzing, Helmut, and Skowroński, Andrzej. "Roots of Nakayama and Auslander-Reiten translations." Colloquium Mathematicae 86.2 (2000): 209-230. <http://eudml.org/doc/210851>.

@article{Lenzing2000,
abstract = {We discuss the roots of the Nakayama and Auslander-Reiten translations in the derived category of coherent sheaves over a weighted projective line. As an application we derive some new results on the structure of selfinjective algebras of canonical type.},
author = {Lenzing, Helmut, Skowroński, Andrzej},
journal = {Colloquium Mathematicae},
keywords = {finite dimensional algebras; quivers; uniserial modules; representations; derived categories; tilting sheaves; concealed-canonical algebras; repetitive algebras; wild algebras},
language = {eng},
number = {2},
pages = {209-230},
title = {Roots of Nakayama and Auslander-Reiten translations},
url = {http://eudml.org/doc/210851},
volume = {86},
year = {2000},
}

TY - JOUR
AU - Lenzing, Helmut
AU - Skowroński, Andrzej
TI - Roots of Nakayama and Auslander-Reiten translations
JO - Colloquium Mathematicae
PY - 2000
VL - 86
IS - 2
SP - 209
EP - 230
AB - We discuss the roots of the Nakayama and Auslander-Reiten translations in the derived category of coherent sheaves over a weighted projective line. As an application we derive some new results on the structure of selfinjective algebras of canonical type.
LA - eng
KW - finite dimensional algebras; quivers; uniserial modules; representations; derived categories; tilting sheaves; concealed-canonical algebras; repetitive algebras; wild algebras
UR - http://eudml.org/doc/210851
ER -

References

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  9. [9] H. Lenzing and H. Meltzer, The automorphism group of the derived category for a weighted projective line, Comm. Algebra 28 (2000), 1685-1700. Zbl0965.16008
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  11. [11] H. Lenzing and A. Skowroński, Selfinjective algebras of wild canonical type, preprint, 1999. 
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  13. [13] Y. Ohnuki, K. Takeda and K. Yamagata, Automorphisms of repetitive algebras, J. Algebra, to appear. Zbl1035.16010
  14. [14] C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, 1984. 
  15. [15] A. Skowroński, Selfinjective algebras of polynomial growth, Math. Ann. 285 (1989), 177-199. Zbl0653.16021
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  17. [17] A. Skowroński and K. Yamagata, Galois coverings of selfinjective algebras by repetitive algebras, Trans. Amer. Math. Soc. 351 (1999), 715-734. Zbl0915.16006

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