We investigate the Galois coverings of piecewise algebras and more particularly their behaviour under derived equivalences. Under a technical assumption which is satisfied if the algebra is derived equivalent to a hereditary algebra, we prove that there exists a universal Galois covering whose group of automorphisms is free and depends only on the derived category of the algebra. As a corollary...

We will give a generalized framework of derived bracket construction. The derived bracket construction provides a method of constructing homotopies. We will prove that a deformation derivation of dg Leibniz algebra (or called dg Loday algebra) induces a strong homotopy Leibniz algebra by the derived bracket method.

Let A be a finite-dimensional k-algebra and K/k finite separable field extension. We prove that is derived equivalent to hereditary algebra if only so ⊗kK.

In this paper we determine the derived representation type of quadratic string algebras and prove that every tame algebra whose quiver has cycles is equivalent to some skewed-gentle algebra.