Endomorphism algebras of tilting modules over m-replicated algebras

Let A be a finite dimensional hereditary algebra over an algebraically closed field k  , and let A(m)A(m) be the m-replicated algebra of A  . In this paper, we investigate the structure properties of the endomorphism algebras of tilting modules of A(m)A(m), and prove that all the endomorphism algebras of tilting modules of A(m)A(m) can be realized as the iterated endomorphism algebras of BB-tilting modules. That is, for each pair of basic tilting A(m)A(m)-modules T1T1 and T2T2 there exists a series of finite dimensional algebras Λ0,Λ1,…,ΛsΛ0,Λ1,…,Λs, which are the endomorphism algebras of some basic tilting A(m)A(m)-modules, and for each ΛiΛi there is a BB-tilting ΛiΛi-module MiMi such that Λ0=EndA(m)T1, Λi=EndΛi−1Mi−1 for 1⩽i⩽s1⩽i⩽s, and EndA(m)T2≃EndΛsMs.