We introduce a new category C, which we call the cluster category, obtained as a quotient of the bounded derived category D of the module category of a finite-dimensional hereditary algebra H over aâ€¦ (More)

We investigate cluster tilting objects (and subcategories) in triangulated 2-Calabi-Yau categories and related categories. In particular we construct a new class of such categories related toâ€¦ (More)

We show that the number of quivers in the mutation class of a quiver of Dynkin type Dn is given by âˆ‘ d|n Ï†(n/d) ( 2d d ) /(2n) for n â‰¥ 5. To obtain this formula, we give a correspondence between theâ€¦ (More)

In the universal composability framework, we define an ideal functionality for blind signatures, as an alternative to a functionality recently proposed by Fischlin. Fischlin proves that hisâ€¦ (More)

Tilting theory provides a good method for comparing two categories, such as module categories of finite-dimensional algebras. For an introduction, see e.g. [A]. BGP reflection functors [BGP] give aâ€¦ (More)

Cluster algebras are commutative algebras that were introduced by Fomin and Zelevinsky in order to model the dual canonical basis of a quantum group and total positivity in algebraic groups. Clusterâ€¦ (More)

We show that the quotient of a Hom-finite triangulated category C by the kernel of the functor HomC(T, âˆ’), where T is a rigid object, is preabelian. We further show that the class of regularâ€¦ (More)

Let W be a finite crystallographic reflection group, with root system Î¦. Associated to W there is a positive integer, the generalized Catalan number, which counts the clusters in the associatedâ€¦ (More)

We introduce a new category C, which we call the cluster category, obtained as a quotient of the bounded derived category D of the module category of a finite-dimensional hereditary algebra H over aâ€¦ (More)

We investigate cluster tilting objects (and subcategories) in triangulated 2-Calabi-Yau categories and related categories. In particular we construct a new class of such categories related toâ€¦ (More)