On quasitilted algebras which are one-point extensions of hereditary algebras

Dieter Happel; Inger Slungård

Colloquium Mathematicae (1999)

  • Volume: 81, Issue: 1, page 141-152
  • ISSN: 0010-1354

Abstract

top
Quasitilted algebras have been introduced as a proper generalization of tilted algebras. In an earlier article we determined necessary conditions for one-point extensions of decomposable finite-dimensional hereditary algebras to be quasitilted and not tilted. In this article we study algebras satisfying these necessary conditions in order to investigate to what extent the conditions are sufficient.

How to cite

top

Happel, Dieter, and Slungård, Inger. "On quasitilted algebras which are one-point extensions of hereditary algebras." Colloquium Mathematicae 81.1 (1999): 141-152. <http://eudml.org/doc/210724>.

@article{Happel1999,
abstract = {Quasitilted algebras have been introduced as a proper generalization of tilted algebras. In an earlier article we determined necessary conditions for one-point extensions of decomposable finite-dimensional hereditary algebras to be quasitilted and not tilted. In this article we study algebras satisfying these necessary conditions in order to investigate to what extent the conditions are sufficient.},
author = {Happel, Dieter, Slungård, Inger},
journal = {Colloquium Mathematicae},
keywords = {quasitilted algebras; one-point extensions; hereditary algebras},
language = {eng},
number = {1},
pages = {141-152},
title = {On quasitilted algebras which are one-point extensions of hereditary algebras},
url = {http://eudml.org/doc/210724},
volume = {81},
year = {1999},
}

TY - JOUR
AU - Happel, Dieter
AU - Slungård, Inger
TI - On quasitilted algebras which are one-point extensions of hereditary algebras
JO - Colloquium Mathematicae
PY - 1999
VL - 81
IS - 1
SP - 141
EP - 152
AB - Quasitilted algebras have been introduced as a proper generalization of tilted algebras. In an earlier article we determined necessary conditions for one-point extensions of decomposable finite-dimensional hereditary algebras to be quasitilted and not tilted. In this article we study algebras satisfying these necessary conditions in order to investigate to what extent the conditions are sufficient.
LA - eng
KW - quasitilted algebras; one-point extensions; hereditary algebras
UR - http://eudml.org/doc/210724
ER -

References

top
  1. [ARS] M. Auslander, I. Reiten and S. Smalο, Representation Theory of Artin Algebras, Cambridge Stud. Adv. Math. 36, Cambridge Univ. Press, Cambridge, 1995. 
  2. [Ha] D. Happel, Triangulated Categories in the Representation Theory of Finite-Dimensional Algebras, London Math. Soc. Lecture Note Ser. 119, Cambridge Univ. Press, Cambridge-New York, 1988. Zbl0635.16017
  3. [HR1] D. Happel and I. Reiten, Directing objects in hereditary categories, in: Contemp. Math. 229, Amer. Math. Soc., Proviedence, RI, 1998, 169-179. Zbl0923.16012
  4. [HR2] D. Happel and I. Reiten, Hereditary categories with tilting object, Math. Z., to appear. 
  5. [HRS] D. Happel, I. Reiten and S. O. Smalο, Tilting in abelian categories and quasitilted algebras, Mem. Amer. Math. Soc. 575 (1996). Zbl0849.16011
  6. [HS] D. Happel and I. H. Slungård, One-point extensions of hereditary algebras, in: Algebras and Modules, II (Geiranger, 1996), CMS Conf. Proc. 24, Amer. Math. Soc., Providence, RI, 1998, 285-291. 
  7. [Hü] T. Hübner, Exzeptionelle Vektorbündel und Reflektionen an Kippgarben über projektiven gewichteten Kurven, dissertation, Universität-GH Paderborn, 1996. 
  8. [LM] H. Lenzing and H. Meltzer, Tilting sheaves and concealed-canonical algebras, in: Representation Theory of Algebras (Cocoyoc, 1994), CMS Conf. Proc. 18, Amer. Math. Soc., Providence, RI, 1996, 455-473. Zbl0863.16013
  9. [LP] H. Lenzing and J. A. de la Pe na, Wild canonical algebras, Math. Z. 224 (1997), 403-425. 
  10. [LS] H. Lenzing and A. Skowroński, Quasitilted algebras of cannonical type, Colloq. Math. 71 (1996), 161-181. 
  11. [Ri] C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, Berlin-New York, 1984. 
  12. [Sk] A. Skowroński, Tame quasitilted algebras, J. Algebra 203 (1998), 470-490. Zbl0908.16013

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.