Tilting modules over duplicated algebras

الأصل · EN

Let A be a finite dimensional hereditary algebra over a field k and A⁽¹⁾ the duplicated algebra of A. We first show that the global dimension of endomorphism ring of tilting modules of A⁽¹⁾ is at most 3. Then we investigate embedding tilting quiver K(A) of A into tilting quiver K(A⁽¹⁾) of A⁽¹⁾. As applications, we give new proofs for some results of D.Happel and L.Unger, and prove that every connected component in K(A) has finite non-saturated points if A is tame type, which gives a partially positive answer to the conjecture of D.Happel and L.Unger in [10]. Finally, we also prove that the number of arrows in K(A) is a constant which does not depend on the orientation of Q if Q is Dynkin type.