Directing components for quasitilted algebras

• Autorzy: Flávio Ulhoa Coelho
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Auslander-Reiten quivers   quasitilted algebras  

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1999
• Tom: 82
• Numer: 2
• Strony: 271-275

Daty

wydano

1999

otrzymano

1999-03-22

otrzymano

1999-06-14

Twórcy

autor

Flávio Ulhoa Coelho

• Departamento de Matemática-IME, Universidade de São Paulo, CP 66281, São Paulo, SP, 05315-970, Brazil

Bibliografia

• [1] M. Auslander, I. Reiten and S. O. Smalο, Representation Theory of Artin Algebras, Cambridge Univ. Press, 1995.
• [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.
• [3] F. U. Coelho and D. Happel, Quasitilted algebras admit a preprojective component, Proc. Amer. Math. Soc. 125 (1997), 1283-1291.
• [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.
• [5] F. U. Coelho, Ma. I. R. Martins and J. A. de la Peña, Quasitilted extensions of algebras II, J. Algebra, to appear.
• [6] F. U. Coelho and A. Skowroński, On Auslander-Reiten components for quasitilted algebras, Fund. Math. 149 (1996), 67-82.
• [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.
• [8] D. Happel, I. Reiten and S. Smalο, Tilting in abelian categories and quasitilted algebras, Mem. Amer. Math. Soc. 575 (1996).
• [9] D. Happel and C. Ringel, Tilted algebras, Trans. Amer. Math. Soc. 274 (1982), 399-443.
• [10] H. Lenzing and A. Skowroński, Quasi-tilted algebras of canonical type, Colloq. Math. 71 (1996), 161-181.
• [11] S. Liu, The connected components of the Auslander-Reiten quiver of a tilted algebra, J. Algebra 61 (1993), 505-523.
• [12] J. A. de la Peña and I. Reiten, Trisection of module categories, to appear.
• [13] A. Skowroński, Tame quasi-tilted algebras, J. Algebra 203 (1998), 470-490.