Piecewise hereditary algebras under field extensions

Skew group algebras of piecewise hereditary algebras are piecewise hereditary

The aim of this paper is twofold. First, we show that the main results of HappelRickard-Schofield (1988) and Happel-Reiten-Smalø (1996) on piecewise hereditary algebras are coherent with the notion of group action on an algebra. Then, we take advantage of this compatibility and show that if G is a finite group acting on a piecewise hereditary algebra A over an algebraically closed field whose c...

Topological Invariants of Piecewise Hereditary Algebras

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...

Derived and Stable Equivalence Classification of Twisted Multifold Extensions of Piecewise Hereditary Algebras of Tree Type

Derived equivalence classification of generalized multifold extensions of piecewise hereditary algebras of tree type

We give a derived equivalence classification of algebras of the form Â/〈φ〉 for some piecewise hereditary algebra A of tree type and some automorphism φ of  such that φ(A) = A for some positive integer n.

The strong global dimension of piecewise hereditary algebras

Let T be a tilting object in a triangulated category which is equivalent to the bounded derived category of a finite-dimensional hereditary algebra. The text investigages the strong global dimension, in the sense of Ringel, of the opposite algebra A of the endomorphism algebra of T . This invariant is expressed in terms of the lengths of the sequences T0, . . . , Tl of tilting objects such that...