Classification of discrete derived categories
Grzegorz Bobiński ; Christof Geiß ; Andrzej Skowroński
Open Mathematics, Tome 2 (2004), p. 19-49 / Harvested from The Polish Digital Mathematics Library

The main aim of the paper is to classify the discrete derived categories of bounded complexes of modules over finite dimensional algebras.

Publié le : 2004-01-01
EUDML-ID : urn:eudml:doc:268791
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     author = {Grzegorz Bobi\'nski and Christof Gei\ss\ and Andrzej Skowro\'nski},
     title = {Classification of discrete derived categories},
     journal = {Open Mathematics},
     volume = {2},
     year = {2004},
     pages = {19-49},
     zbl = {1036.18007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475948}
}
Grzegorz Bobiński; Christof Geiß; Andrzej Skowroński. Classification of discrete derived categories. Open Mathematics, Tome 2 (2004) pp. 19-49. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475948/

[1] I. Assem and D. Happel: “Generalized tilted algebras of type 𝔸n ”, Comm. Algebra, Vol. 9, (1981), pp. 2101–2125. | Zbl 0481.16009

[2] I. Assem and A. Skowroński: “Iterated tilted algebras of type 𝔸˜n ”, Math. Z., Vol. 195, (1987), pp. 269–290. http://dx.doi.org/10.1007/BF01166463 | Zbl 0601.16022

[3] I. Assem and A. Skowroński: “Algebras with cycle-finite derived categories”, Math. Ann., Vol. 280, (1988), pp. 441–463. http://dx.doi.org/10.1007/BF01456336 | Zbl 0617.16017

[4] M. Auslander, M. Platzeck and I. Reiten: “Coxeter functors without diagrams”, Trans. Amer. Math. Soc., Vol. 250, (1979), pp. 1–46. http://dx.doi.org/10.2307/1998978

[5] M. Barot and J. A. de la Peña: “The Dynkin type of non-negative unit form”, Expo. Math., Vol. 17, (1999), pp. 339–348. | Zbl 1073.15531

[6] K. Bongartz: “Tilted Algebras”, Lecture Notes in Math., Vol. 903, (1981), pp. 26–38.

[7] K. Bongartz and P. Gabriel: “Covering spaces in representation theory”, Invent. Math., Vol. 65, (1981), pp. 331–378. http://dx.doi.org/10.1007/BF01396624 | Zbl 0482.16026

[8] M. C. R. Butler and C. M. Ringel: “Auslander-Reiten sequences with few middle terms and applications to string algebras”, Comm. Algebra, Vol. 15, (1987), pp. 145–179. | Zbl 0612.16013

[9] Ch. Geiß and J. A. de la Peña: “Auslander-Reiten components for clans”, Bol. Soc. Mat. Mexicana, Vol. 5, (1999), pp. 307–326. | Zbl 0959.16013

[10] D. Happel: Triangulated categories in the representation theory of finite-dimensional algebras, London Math. Soc. Lecture Note Series, 1988. | Zbl 0635.16017

[11] D. Happel: “Auslander-Reiten triangles in derived categories of finite-dimensional algebras”, Proc. Amer. Math. Soc., Vol. 112, (1991), pp. 641–648. http://dx.doi.org/10.2307/2048684 | Zbl 0736.16005

[12] D. Happel and C. M. Ringel: “Tilted algebras”, Trans. Amer. Math. Soc., Vol. 274, (1982), pp. 399–443. http://dx.doi.org/10.2307/1999116 | Zbl 0503.16024

[13] D. Hughes and J. Waschbüsch: “Trivial extensions of tilted algebras”, Proc. London Math. Soc., Vol. 46, (1983), pp. 347–364. | Zbl 0488.16021

[14] B. Keller and D. Vossieck: “Aisles in derived, categories”, Bull. Soc. Math. Belg., Vol. 40, (1988), pp. 239–253. | Zbl 0671.18003

[15] J. Nehring: “Polynomial growth trivial extensions of non-simply connected algebras”, Bull. Polish Acad. Sci. Math., Vol. 36, (1988), pp. 441–445. | Zbl 0777.16008

[16] J. Rickard: “Morita theory for derived categories”, J. London Math. Soc., Vol. 39, (1989), pp. 436–456. | Zbl 0642.16034

[17] C. M. Ringel: Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math., 1984.

[18] C. M. Ringel: “The repetitive algebra of a gentle algebra”, Bol. Soc. Mat. Mexicana, Vol. 3, (1997), pp. 235–253. | Zbl 0906.16005

[19] A. Skowroński and J. Waschbüsch: “Representation-finite biserial algebras”, J. Reine Angew. Math., Vol. 345, (1983), pp. 172–181. | Zbl 0511.16021

[20] J. L. Verdier: “Categories derivées, état 0”, Lecture Notes in Math., Vol. 569, (1977), pp. 262–331.

[21] D. Vossieck: “The algebras with discrete derived category”, J. Algebra, Vol. 243, (2001), pp. 168–176. http://dx.doi.org/10.1006/jabr.2001.8783

[22] H. Tachikawa and T. Wakamatsu: “Applications of reflection functors for selfinjective algebras”, Lecture Notes in Math., Vol. 1177, (1986), pp. 308–327. http://dx.doi.org/10.1007/BFb0075271 | Zbl 0626.16016