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A finite poset X carries a natural structure of a topological space. Fix a field k, and denote by D(X) the bounded derived category of sheaves of finite dimensional k-vector spaces over X. Two posets X and Y are said to be derived equivalent if D(X) and D(Y ) are equivalent as triangulated categories. We give explicit combinatorial properties of X which are… (More)

- Sefi Ladkani
- 2007

We show that for piecewise hereditary algebras, the periodicity 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)

- Sefi Ladkani
- J. London Math. Society
- 2013

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)

- Sefi Ladkani
- 2008

We show that for two quivers without oriented cycles related by a BGP reflection, the posets of their tilting modules are related by a simple combinatorial construction, which we call flip-flop. We deduce that the posets of tilting modules of derived equivalent path algebras of quivers without oriented cycles are universally derived equivalent.

- Sefi Ladkani
- 2008

We show that for two quivers without oriented cycles related by a BGP reflection, the posets of their cluster tilting objects are related by a simple combinatorial construction, which we call a flip-flop. We deduce that the posets of cluster tilting objects of derived equivalent path algebras of quivers without oriented cycles are universally derived… (More)

- Sefi Ladkani
- 2008

We give a full description of all the canonical algebras over an algebraically closed field that are derived equivalent to incidence algebras of finite posets. These are the canonical algebras of weight type other than (1, p) whose number of weights does not exceed 3. This note concerns the characterization of the canonical algebras over an algebraically… (More)

- Sefi Ladkani
- 2008

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 functor induces a triangulated functor between the corresponding derived categories. This allows us to… (More)

- Sefi Ladkani
- 2013

We show that many cluster-theoretic properties of the Markov quiver hold also for adjacency quivers of triangulations of once-punctured closed surfaces of arbitrary genus. Along the way we consider the class P of quivers introduced by Kontsevich and Soibelman, characterize the mutation-finite quivers that belong to that class and draw some conclusions… (More)

- Chris Brav, David Ploog, Brian Jurgelewicz, Bernhard Keller, Helmut Lenzing, Sefi Ladkani
- 2010

A Coxeter element is a special isometry defined for some free abelian groups with a (not necessarily symmetric) bilinear pairing. For example, for a lattice with a basis of roots (i.e. vectors of square −2), the Coxeter element is the product of reflections along the basis roots. It depends on the ordering of the basis, but a permutation of the basis will… (More)

- Sefi Ladkani
- 2008

A triangular matrix ring Λ is defined by a triplet (R, S, M) where R and S are rings and RMS 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)