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- SEFI LADKANI, D. Kazhdan
- 2006

A finite poset X carries a natural structure of a topological space. Fix a field k, and denote by D b (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 b (X) and D b (Y) are equivalent as triangulated categories. We give explicit combinatorial properties of X… (More)

- SEFI LADKANI
- 2007

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)

- 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 func-tor induces a triangulated functor between the corresponding derived categories. This allows us… (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

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)

- 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
- 2009

We provide a categorical interpretation of a well-known identity from linear algebra as an isomorphism of certain functors between triangulated categories arising from finite dimensional algebras. As a consequence, we deduce that the Serre functor of a finite dimensional triangular algebra A has always a lift, up to shift, to a product of suitably defined… (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
- 2007

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)

- 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)