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We show that for piecewise hereditary algebras, the pe-riodicity of the Coxeter transformation implies the non-negativity of the Euler form. Contrary to previous assumptions, the condition of piecewise heredity cannot be omitted, even for triangular algebras, as demonstrated by incidence algebras of posets. We also give a simple, direct proof, that certain(More)
By using only combinatorial data on two posets X and Y , we construct a set of so-called formulas. A formula produces simultaneously , for any abelian category A, a functor between the categories of complexes of diagrams over X and Y with values in A. This func-tor induces a triangulated functor between the corresponding derived categories. This allows us(More)
We present a method to construct new tilting complexes from existing ones using tensor products, generalizing a result of Rickard. The endomorphism rings of these complexes are generalized matrix rings that are " componentwise " tensor products, allowing us to obtain many derived equivalences that have not been observed by using previous techniques.(More)
A triangular matrix ring Λ is defined by a triplet (R, S, M) where R and S are rings and R MS is an S-R-bimodule. In the main theorem of this paper we show that if TS is a tilting S-module, then under certain homological conditions on the S-module MS, one can extend TS to a tilting complex over Λ inducing a derived equivalence between Λ and another(More)
A triangular matrix algebra over a field k is defined by a triplet (R, S, M) where R and S are k-algebras and R MS is an S-R-bimodule. We show that if R, S and M are finite dimensional and the global dimensions of R and S are finite, then the triangular matrix algebra corresponding to (R, S, M) is derived equivalent to the one corresponding to (S, R, DM),(More)