Constructing the directing components of an algebra

J. de la Peña; M. Takane

Colloquium Mathematicae (1997)

  • Volume: 74, Issue: 1, page 29-46
  • ISSN: 0010-1354

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de la Peña, J., and Takane, M.. "Constructing the directing components of an algebra." Colloquium Mathematicae 74.1 (1997): 29-46. <http://eudml.org/doc/210500>.

@article{delaPeña1997,
author = {de la Peña, J., Takane, M.},
journal = {Colloquium Mathematicae},
keywords = {directing components; one-point extensions; finite dimensional algebras; Auslander-Reiten quivers; connected components; indecomposable modules; convex subcategories},
language = {eng},
number = {1},
pages = {29-46},
title = {Constructing the directing components of an algebra},
url = {http://eudml.org/doc/210500},
volume = {74},
year = {1997},
}

TY - JOUR
AU - de la Peña, J.
AU - Takane, M.
TI - Constructing the directing components of an algebra
JO - Colloquium Mathematicae
PY - 1997
VL - 74
IS - 1
SP - 29
EP - 46
LA - eng
KW - directing components; one-point extensions; finite dimensional algebras; Auslander-Reiten quivers; connected components; indecomposable modules; convex subcategories
UR - http://eudml.org/doc/210500
ER -

References

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  1. [1] M. Auslander, I. Reiten and S. Smalο, Representation Theory of Artin Algebras, Cambridge Stud. Adv. Math. 36, Cambridge Univ. Press, 1995. 
  2. [2] R. Bautista, F. Larrión and L. Salmerón, On simply connected algebras, J. London Math. Soc. (2) 27 (2) (1983), 212-220. Zbl0511.16022
  3. [3] F. Coelho and D. Happel, Quasitilted algebras admit a preprojective component, to appear. Zbl0880.16006
  4. [4] P. Dräxler and J. A. de la Pe na, On the existence of postprojective components for algebras, Tsukuba J. Math. 20 (1996), 457-469. Zbl0902.16017
  5. [5] P. Gabriel, Auslander-Reiten sequences and representation-finite algebras, in: Representation Theory I (Proc. ICRA II, Ottawa, 1979), Lecture Notes in Math. 831, Springer, 1980, 1-71. 
  6. [6] P. Gabriel and J. A. de la Pe na, On algebras: wild and tame, in: Duration and Change. Fifty Years at Oberwolfach, Springer, 1994, 177-210. 
  7. [7] W. Geigle and H. Lenzing, Perpendicular categories with applications to representations and sheaves, J. Algebra 144 (1991), 273-343. 
  8. [8] D. Happel and C. M. Ringel, Directing projective modules, Arch. Math. (Basel) 60 (1993), 237-246. Zbl0795.16007
  9. [9] S. Kasjan and J. A. de la Pe na, Constructing the preprojective components of an algebra, J. Algebra 179 (1996), 793-807. Zbl0848.16010
  10. [10] O. Kerner, Tilting wild algebras, J. London Math. Soc. 39 (1989), 29-47. Zbl0675.16013
  11. [11] S. Liu, Tilted algebras and generalized standard Auslander-Reiten components, Arch. Math. (Basel) 61 (1993), 12-19. Zbl0809.16015
  12. [12] J. A. de la Pe na and M. Takane, Spectral properties of Coxeter transformations and applications, ibid. 55 (1990), 120-134. Zbl0687.16017
  13. [13] C. M. Ringel, Tame algebras, in: Representation Theory I (Proc. ICRA II, Ottawa, 1979), Lecture Notes in Math. 831, Springer, 1980, 137-287. 
  14. [14] C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, Berlin, 1984. 
  15. [15] C. M. Ringel, The spectral radius of the Coxeter transformation for a generalized Cartan matrix, Math. Ann. 300 (1994), 331-339. 
  16. [16] A. Skowroński, Cycles in module categories, in: Finite Dimensional Algebras and Related Topics, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 424, Kluwer, 1994, 309-345. Zbl0819.16013
  17. [17] A. Skowroński, Generalized standard Auslander-Reiten components without oriented cycles, Osaka J. Math. 30 (1993), 515-527. Zbl0818.16017
  18. [18] A. Skowroński and S. Smalο, Directing modules, J. Algebra 147 (1992), 137-146. Zbl0746.16008
  19. [19] A. Skowroński and M. Wenderlich, Artin algebras with directing indecomposable projective modules, ibid. 165 (1994), 507-530. Zbl0841.16014
  20. [20] H. Strauß, On the perpendicular category of a partial tilting module, ibid. 144 (1991), 43-66. Zbl0746.16009

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