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)
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 address the question of when cluster-tilted algebras of Dynkin type E are derived equivalent and as main result obtain a complete derived equivalence classification. It turns out that two cluster-tilted algebras of type E are derived equivalent if and only if their Cartan matrices represent equivalent bilinear forms over the integers. For type E6 all(More)