Directing components for quasitilted algebras

Flávio Coelho

Colloquium Mathematicae (1999)

  • Volume: 82, Issue: 2, page 271-275
  • ISSN: 0010-1354

Abstract

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We show here that a directing component of the Auslander-Reiten quiver of a quasitilted algebra is either postprojective or preinjective or a connecting component.

How to cite

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Coelho, Flávio. "Directing components for quasitilted algebras." Colloquium Mathematicae 82.2 (1999): 271-275. <http://eudml.org/doc/210764>.

@article{Coelho1999,
abstract = {We show here that a directing component of the Auslander-Reiten quiver of a quasitilted algebra is either postprojective or preinjective or a connecting component.},
author = {Coelho, Flávio},
journal = {Colloquium Mathematicae},
keywords = {Auslander-Reiten quivers; quasitilted algebras; tilted algebras; directing modules; finite dimensional algebras; categories of finitely generated modules; injective dimensions; projective dimensions; global dimensions},
language = {eng},
number = {2},
pages = {271-275},
title = {Directing components for quasitilted algebras},
url = {http://eudml.org/doc/210764},
volume = {82},
year = {1999},
}

TY - JOUR
AU - Coelho, Flávio
TI - Directing components for quasitilted algebras
JO - Colloquium Mathematicae
PY - 1999
VL - 82
IS - 2
SP - 271
EP - 275
AB - We show here that a directing component of the Auslander-Reiten quiver of a quasitilted algebra is either postprojective or preinjective or a connecting component.
LA - eng
KW - Auslander-Reiten quivers; quasitilted algebras; tilted algebras; directing modules; finite dimensional algebras; categories of finitely generated modules; injective dimensions; projective dimensions; global dimensions
UR - http://eudml.org/doc/210764
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] S. Brenner and M. Butler, Generalizations of the Bernstein-Gelfand-Ponomarev reflection functors, in: Proc. ICRA II, Lecture Notes in Math. 832, Springer, 1980, 103-169. Zbl0446.16031
  3. [3] F. U. Coelho and D. Happel, Quasitilted algebras admit a preprojective component, Proc. Amer. Math. Soc. 125 (1997), 1283-1291. Zbl0880.16006
  4. [4] F. U. Coelho, Ma. I. R. Martins and J. A. de la Peña, Quasitilted extensions of algebras I, Proc. Amer. Math. Soc., to appear. Zbl0970.16009
  5. [5] F. U. Coelho, Ma. I. R. Martins and J. A. de la Peña, Quasitilted extensions of algebras II, J. Algebra, to appear. 
  6. [6] F. U. Coelho and A. Skowroński, On Auslander-Reiten components for quasitilted algebras, Fund. Math. 149 (1996), 67-82. Zbl0848.16012
  7. [7] P. Dräxler and J. A. de la Peña, On the existence of postprojective components in the Auslander-Reiten quiver of an algebra, Tsukuba J. Math. 20 (1996), 457-469. Zbl0902.16017
  8. [8] D. Happel, I. Reiten and S. Smalο, Tilting in abelian categories and quasitilted algebras, Mem. Amer. Math. Soc. 575 (1996). Zbl0849.16011
  9. [9] D. Happel and C. Ringel, Tilted algebras, Trans. Amer. Math. Soc. 274 (1982), 399-443. 
  10. [10] H. Lenzing and A. Skowroński, Quasi-tilted algebras of canonical type, Colloq. Math. 71 (1996), 161-181. Zbl0870.16007
  11. [11] S. Liu, The connected components of the Auslander-Reiten quiver of a tilted algebra, J. Algebra 61 (1993), 505-523. Zbl0818.16014
  12. [12] J. A. de la Peña and I. Reiten, Trisection of module categories, to appear. 
  13. [13] A. Skowroński, Tame quasi-tilted algebras, J. Algebra 203 (1998), 470-490. Zbl0908.16013

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