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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
DOI: https://doi.org/10.1090/S0002-9939-99-05230-2
Published electronically: November 29, 1999
MathSciNet review: 1653413
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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.


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Additional Information

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: https://doi.org/10.1090/S0002-9939-99-05230-2
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
Published electronically: November 29, 1999
Communicated by: Ken Goodearl
Article copyright: © Copyright 2000 American Mathematical Society

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