Quasitilted algebras have preprojective components

Ole Enge

Colloquium Mathematicae (2000)

  • Volume: 83, Issue: 1, page 55-69
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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Enge, Ole. "Quasitilted algebras have preprojective components." Colloquium Mathematicae 83.1 (2000): 55-69. <http://eudml.org/doc/210773>.

@article{Enge2000,
abstract = {We show that a quasitilted algebra has a preprojective component. This is proved by giving an algorithmic criterion for the existence of preprojective components.},
author = {Enge, Ole},
journal = {Colloquium Mathematicae},
keywords = {preprojective components; quasi-tilted algebras; quivers},
language = {eng},
number = {1},
pages = {55-69},
title = {Quasitilted algebras have preprojective components},
url = {http://eudml.org/doc/210773},
volume = {83},
year = {2000},
}

TY - JOUR
AU - Enge, Ole
TI - Quasitilted algebras have preprojective components
JO - Colloquium Mathematicae
PY - 2000
VL - 83
IS - 1
SP - 55
EP - 69
AB - We show that a quasitilted algebra has a preprojective component. This is proved by giving an algorithmic criterion for the existence of preprojective components.
LA - eng
KW - preprojective components; quasi-tilted algebras; quivers
UR - http://eudml.org/doc/210773
ER -

References

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  1. [1] M. Auslander, I. Reiten and S. O. Smalο, Representation Theory of Artin Algebras, Cambridge Univ. Press, 1995. Zbl0834.16001
  2. [2] B K. Bongartz, A criterion for finite representation type, Math. Ann. 269 (1984), 1-12. Zbl0552.16012
  3. [3] F. Coelho and D. Happel, Quasitilted algebras admit a preprojective component, Proc. Amer. Math. Soc. 125 (1997), 1283-1291. Zbl0880.16006
  4. [4] F. Coelho and A. Skowroński, On Auslander-Reiten components for quasitilted algebras, Fund. Math. 149 (1996), 67-82. Zbl0848.16012
  5. [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. Zbl0902.16017
  6. [6] O. Enge, I. H. Slungård and S. O. Smalο, Quasitilted extensions by nondirecting modules, preliminary manuscript, 1998. 
  7. [7] D. Happel, I. Reiten and S. O. Smalο, Tilting in abelian categories and quasitilted algebras, Mem. Amer. Math. Soc. 575 (1996). Zbl0849.16011
  8. [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. Zbl0828.16009
  9. [9] D. Happel and C. M. Ringel, Directing projective modules, Arch. Math. (Basel) 60 (1993), 237-246. Zbl0795.16007
  10. [10] A. Skowroński and M. Wenderlich, Artin algebras with directing indecomposable projective modules, J. Algebra 165 (1994), 507-530. Zbl0841.16014
  11. [11] H. Strauss, The perpendicular category of a partial tilting module, ibid. 144 (1991), 43-66. Zbl0746.16009

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