Proceedings of the American Mathematical Society

Author(s): Ibrahim Assem; Dieter Happel; Sonia Trepode
Journal: Proc. Amer. Math. Soc. 128 (2000), 2223-2232.
MSC (2000): Primary 16G60, 16G20
Posted: November 29, 1999
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Abstract: We show that, if

is a representation-finite iterated tilted algebra of euclidean type

, then there exist a sequence of algebras $A=A_{0},A_{1},A_{2},\dots, A_{m}$ , and a sequence of modules $T^{(i)}_{A_{i}}$ , where $0\leq i<m$ , such that each $T^{(i)}_{A_{i}}$ is an APR-tilting $A_{i}$ -module, or an APR-cotilting $A_{i}$ -module, $\operatorname{End} T^{(i)}_{A_{i}}=A_{i+1}$ and $A_{m}$ is tilted representation-finite.

1.: Assem, I., Tilting theory - an introduction, in: ``Topics in Algebra'', vol. 26, Banach Center Publications, PWN, Warsaw, 1990, p. 127-180. MR 93g:16011
2.: Assem, I. and Happel, D., Generalized tilted algebras of type ${\mathbb{A}}_{n}$ , vol. 9, Comm. Algebra, 1981, p. 2101-2125. MR 83a:16023a
3.: Assem, I. and Skowro\'{n}ski, A., Iterated tilted algebras of type $\tilde {\mathbb{A}}_{n}$ , vol. 195, Math. Z, 1987, p. 269-290. MR 88m:16033
4.: Assem, I. and Zhang, Y., Endomorphism algebras of exceptional sequences over path algebras of type $\tilde {\mathbb{A}}_{n}$ , Colloq. Math. 77 (1998), 271-292. CMP 98:14
5.: Auslander, M., Reiten, I. and Smalø,S.O., Representation theory of artin algebras, vol. 36, Cambridge studies in advanced mathematics, Cambridge University Press, 1995. MR 96c:16015
6.: Dlab, V. and Ringel, C.M., Indecomposable representations of graphs and algebras, vol. 6, 173, Memoir Amer. Math. Soc, 1976. MR 56:5657
7.: Happel, D., Triangulated categories in the representation theory of finite dimensional algebras, London Math. Soc. Lecture Note Series 119, 1988. MR 89e:16035
8.: Richard, J., A Morita theory for derived categories, vol. 2, 39, J. London Math. Soc., 1989, p. 436-456.
9.: Ringel, C. M., Tame algebras and integral quadratic forms, vol. 1099, Lecture Notes in Mathematics, Springer-Verlag, Berlin - Heidelberg- New York., 1984. MR 87f:16027
10.: Roldán, O., Tilted algebras of types $\tilde {\mathbb{A}}_{n}$ , $\tilde {\mathbb{B}}_{n}$ , $\tilde {\mathbb{C}}_{n}$ and $\widetilde {{\mathbb{B}}{\mathbb{C}}}_{n}$ , Ph. D. Thesis, Carleton University (1983).
11.: Skowro\'{n}ski, A., Selfinjective algebras of polynomial growth, vol. 285, Math. Ann, 1989, p. 177- 199. MR 90k:16024
12.: Trepode, S.E., A conjectura de Roldán para álgebras inclinadas iteradas de tipo euclideano, Ph. D. Thesis, Universidade de São Paulo, 1995.
13.: Trepode, S.E., La conjetura de Roldán en el caso $\tilde {\mathbb{A}}_{n}$ , Proc. of the 3rd Conf. of Mathematics Dr. A.A. Monteiro, Bahia Blanca, Argentina, Universidad Nacional del Sur, (1996), p. 51-68. MR 98e:16016

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Ibrahim Assem
Affiliation: Département de mathématiques et d'informatique, Faculté des sciences, Université de Sherbrooke, Québec, Canada J1K 2R1
Email: ibrahim.assem@dmi.usherb.ca

Dieter Happel
Affiliation: Fakultät für Mathematik, TU Chemmitz, PSF 964, D-09107 Chemnitz, Federal Republic of Germany
Email: happel@mathematik.tu-chemnitz.de

Sonia Trepode
Affiliation: Departamento de Matemáticas, Facultad de Ciencias Exactas y Naturales, Universidad nacional de Mar del Plata, Funes 3350, 7600 Mar del Plata, Argentina
Address at time of publication: Instituto de Matemáticas, UNAM, Circuito exterior, Cd. Universitaria, México, 04510 D.F., Mexico
Email: strepode@ mdp.edu.ar, sonia@math.unam.mx

DOI: 10.1090/S0002-9939-99-05230-2
PII: S 0002-9939(99)05230-2
Keywords: Representation-finite iterated tilted algebras of euclidean type, APR-tilting and cotilting modules, derived category
Received by editor(s): December 15, 1997
Received by editor(s) in revised form: September 10, 1998
Posted: November 29, 1999
Communicated by: Ken Goodearl
Copyright of article: Copyright 2000, American Mathematical Society

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