Tilting up iterated tilted algebras

Abstract

We show that, if A A is a representation-finite iterated tilted algebra of euclidean type Q Q , then there exist a sequence of algebras A = A 0 , A 1 , A 2 , … , A m A=A_{0},A_{1},A_{2},\dots , A_{m} , and a sequence of modules T A i ( i ) T^{(i)}_{A_{i}} , where 0 ≤ i > m 0\leq i>m , such that each T A i ( i ) T^{(i)}_{A_{i}} is an APR-tilting A i A_{i} -module, or an APR-cotilting A i A_{i} -module, End ⁡ T A i ( i ) = A i + 1 \operatorname {End} T^{(i)}_{A_{i}}=A_{i+1} and A m A_{m} is tilted representation-finite.