Tilting up iterated tilted algebras

Assem, Ibrahim; Happel, Dieter; Trepode, Sonia

doi:10.1090/S0002-9939-99-05230-2

Tilting up iterated tilted algebras
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by Ibrahim Assem, Dieter Happel and Sonia Trepode PDF

Proc. Amer. Math. Soc. 128 (2000), 2223-2232 Request permission

Abstract:

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