Quasitilted algebras have preprojective components
Enge, Ole
Colloquium Mathematicae, Tome 84/85 (2000), p. 55-69 / Harvested from The Polish Digital Mathematics Library
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We show that a quasitilted algebra has a preprojective component. This is proved by giving an algorithmic criterion for the existence of preprojective components.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:210773 
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     author = {Ole Enge},
     title = {Quasitilted algebras have preprojective components},
     journal = {Colloquium Mathematicae},
     volume = {84/85},
     year = {2000},
     pages = {55-69},
     zbl = {0962.16011},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv83i1p55bwm}
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Enge, Ole. Quasitilted algebras have preprojective components. Colloquium Mathematicae, Tome 84/85 (2000) pp. 55-69. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv83i1p55bwm/

[000] [1] M. Auslander, I. Reiten and S. O. Smalο, Representation Theory of Artin Algebras, Cambridge Univ. Press, 1995. | Zbl 0834.16001

[001] [2] B K. Bongartz, A criterion for finite representation type, Math. Ann. 269 (1984), 1-12. | Zbl 0552.16012

[002] [3] F. Coelho and D. Happel, Quasitilted algebras admit a preprojective component, Proc. Amer. Math. Soc. 125 (1997), 1283-1291. | Zbl 0880.16006

[003] [4] F. Coelho and A. Skowroński, On Auslander-Reiten components for quasitilted algebras, Fund. Math. 149 (1996), 67-82. | Zbl 0848.16012

[004] [5] P. Dräxler and J. A. de la Pe na, On the existence of postprojective components in the Auslander-Reiten quiver of an algebra, Tsukuba J. Math. 20 (1996), 457-469. | Zbl 0902.16017

[005] [6] O. Enge, I. H. Slungård and S. O. Smalο, Quasitilted extensions by nondirecting modules, preliminary manuscript, 1998.

[006] [7] D. Happel, I. Reiten and S. O. Smalο, Tilting in abelian categories and quasitilted algebras, Mem. Amer. Math. Soc. 575 (1996). | Zbl 0849.16011

[007] [8] D. Happel, I. Reiten and S. O. Smalο, Short cycles and sincere modules, in: CMS Conf. Proc. 14, Amer. Math. Soc., 1993, 233-237. | Zbl 0828.16009

[008] [9] D. Happel and C. M. Ringel, Directing projective modules, Arch. Math. (Basel) 60 (1993), 237-246. | Zbl 0795.16007

[009] [10] A. Skowroński and M. Wenderlich, Artin algebras with directing indecomposable projective modules, J. Algebra 165 (1994), 507-530. | Zbl 0841.16014

[010] [11] H. Strauss, The perpendicular category of a partial tilting module, ibid. 144 (1991), 43-66. | Zbl 0746.16009