Sefi Ladkani

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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 compute the Hochschild cohomology groups of the cluster-tilted algebras of finite representation type. An important homological invariant of a finite-dimensional algebra Λ over a field K is its Hochschild cohomology, defined as the graded ring HH * (Λ) = Ext * Λ op ⊗ K Λ (Λ, Λ), see [14]. Even if Λ is given combinatorially as quiver with relations, it is(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)
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)