ENDOMORPHISM ALGEBRAS OF PREPROJECTIVE PARTIAL TILTING MODULES

Let be a connected finite quiver without oriented cycle, A=k(?) the corresponding path algebra with k being an algebraically closed field, A~T a preprojective tilting module. B=EndT. Then B is called a tame (resp. wild)concealed algebra provided is an Euclidean (resp. wild ) graph. The following result is important in the representation theory of tame concealed algebras (see [1,4.9]): if A is tame concealed, T= T⊕ Ta tilting module with Tnonzero preprojective and Tregular, then EndTis tame concealed. The main purpose of this note is to generalize it to the "wild" case. For this we generally consider the endomorphism algebra of preprojective partial tilting modules over a concealed algebra. For the notations the readers can refer to Ref.[1].