# Roots of Nakayama and Auslander-Reiten translations

Helmut Lenzing; Andrzej Skowroński

Colloquium Mathematicae (2000)

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

## Access Full Article

top## Abstract

top## How to cite

topLenzing, 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

top- [1] I. Assem, J. Nehring and A. Skowroński, Domestic trivial extensions of simply connected algebras, Tsukuba J. Math. 13 (1989), 31-72. Zbl0686.16011
- [2] K. Bongartz, Critical simply connected algebras, Manuscripta Math. 46 (1984), 117-136. Zbl0537.16024
- [3] H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 3rd ed., Springer, 1972. Zbl0239.20040
- [4] W. Geigle and H. Lenzing, A class of weighted projective curves arising in representation theory of finite dimensional algebras, in: Singularities, Representations of Algebras, and Vector Bundles, Lecture Notes in Math. 1273, Springer, 1987, 265-297.
- [5] D. Happel, Triangulated Categories in the Representation Theory of Finite Dimensional Algebras, London Math. Soc. Lecture Note Ser. 119, Cambridge Univ. Press, 1988. Zbl0635.16017
- [6] D. Happel and D. Vossieck, Minimal algebras of infinite representation type with preprojective component, Manuscripta Math. 42 (1983), 221-243. Zbl0516.16023
- [7] D. Hughes and J. Waschbüsch, Trivial extensions of tilted algebras, Proc. London Math. Soc. 46 (1983), 347-364. Zbl0488.16021
- [8] H. Lenzing and H. Meltzer, Sheaves on a weighted projective line of genus one and representations of tubular algebras, in: Representations of Algebras, CMS Conf. Proc. 14, Amer. Math. Soc., 1993, 313-337. Zbl0809.16012
- [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
- [10] H. Lenzing and A. Skowroński, On selfinjective algebras of Euclidean type, Colloq. Math. 79 (1999), 71-76. Zbl0947.16005
- [11] H. Lenzing and A. Skowroński, Selfinjective algebras of wild canonical type, preprint, 1999.
- [12] J. Nehring and A. Skowroński, Polynomial growth trivial extensions of simply connected algebras, Fund. Math. 132 (1989), 117-134. Zbl0677.16008
- [13] Y. Ohnuki, K. Takeda and K. Yamagata, Automorphisms of repetitive algebras, J. Algebra, to appear. Zbl1035.16010
- [14] C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, 1984.
- [15] A. Skowroński, Selfinjective algebras of polynomial growth, Math. Ann. 285 (1989), 177-199. Zbl0653.16021
- [16] A. Skowroński and K. Yamagata, Socle deformations of selfinjective algebras, Proc. London Math. Soc. 72 (1996), 545-566. Zbl0862.16001
- [17] A. Skowroński and K. Yamagata, Galois coverings of selfinjective algebras by repetitive algebras, Trans. Amer. Math. Soc. 351 (1999), 715-734. Zbl0915.16006

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.