TILTING MUTATION FOR m-REPLICATED ALGEBRAS
Let A be a finite-dimensional hereditary algebra over an algebraically closed field k, A(m) be the m-replicated algebra of A and [Formula: see text] be the m-cluster category of A. In this paper, we introduce the notion of mutation team in mod A(m), and prove that each faithful almost complete tilting module over A(m) has a mutation team by showing that the sequence of the complements satisfies the properties of the mutation team. We also prove that for each partial mutation team in the m-left part of mod A(m), there exists a faithful almost complete tilting module having the partial mutation team as the set of indecomposable complements. As an application, we prove that m-cluster mutation in [Formula: see text] can be realized as tilting mutation in mod A(m), and we also give the relationship between connecting sequences in mod A(m) and higher AR-angles in the m-cluster category [Formula: see text].