Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Tilting up iterated tilted algebras

Authors: Ibrahim Assem, Dieter Happel and Sonia Trepode
Journal: Proc. Amer. Math. Soc. 128 (2000), 2223-2232
MSC (2000): Primary 16G60, 16G20
Published electronically: November 29, 1999
MathSciNet review: 1653413
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that, if $A$ is a representation-finite iterated tilted algebra of euclidean type $Q$, then there exist a sequence of algebras $A=A_{0},A_{1},A_{2},\dots,\linebreak A_{m}$, 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.

References [Enhancements On Off] (What's this?)

  • 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 16G60, 16G20

Retrieve articles in all journals with MSC (2000): 16G60, 16G20

Additional Information

Ibrahim Assem
Affiliation: Département de mathématiques et d’informatique, Faculté des sciences, Université de Sherbrooke, Québec, Canada J1K 2R1

Dieter Happel
Affiliation: Fakultät für Mathematik, TU Chemmitz, PSF 964, D-09107 Chemnitz, Federal Republic of Germany

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@,

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
Published electronically: November 29, 1999
Communicated by: Ken Goodearl
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society