Endomorphism algebras of tilting modules over m-replicated algebras

Abstract Let A be a finite dimensional hereditary algebra over an algebraically closed field k , and let 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 ) , and prove that all the endomorphism algebras of tilting modules of A ( m ) can be realized as the iterated endomorphism algebras of BB-tilting modules. That is, for each pair of basic tilting A ( m ) -modules T 1 and T 2 there exists a series of finite dimensional algebras Λ 0 , Λ 1 , … , Λ s , which are the endomorphism algebras of some basic tilting A ( m ) -modules, and for each Λ i there is a BB-tilting Λ i -module M i such that Λ 0 = End A ( m ) T 1 , Λ i = End Λ i − 1 M i − 1 for 1 ⩽ i ⩽ s , and End A ( m ) T 2 ≃ End Λ s M s .