Matrix mutation appears in the definition of cluster algebras of Fomin and Zelevinsky. We give a representation theoretic interpretation of matrix mutation, using tilting theory in cluster categoriesâ€¦ (More)

For the flag variety G/B of a reductive algebraic group G we define and describe explicitly a certain (set-theoretical) cross-section Ï† : G/B â†’ G. The definition of Ï† depends only on a choice ofâ€¦ (More)

We consider quivers/skew-symmetric matrices under the action of mutation (in the cluster algebra sense). We classify those which are isomorphic to their own mutation via a cycle permuting all theâ€¦ (More)

We introduce a new class of algebras, which we call cluster-tilted. They are by definition the endomorphism algebras of tilting objects in a cluster category. We show that their representation theoryâ€¦ (More)

We investigate the cluster-tilted algebras of finite representation type over an algebraically closed field. We give an explicit description of the relations for the quivers for finite representationâ€¦ (More)

We show that the m-cluster category of type A nâˆ’1 is equivalent to a certain geometrically-defined category of diagonals of a regular nm + 2-gon. This generalises a result of Caldero, Chapoton andâ€¦ (More)

We construct frieze patterns of type DN with entries which are numbers of matchings between vertices and triangles of corresponding triangulations of a punctured disc. For triangulationsâ€¦ (More)

We construct frieze patterns of type D N with entries which are numbers of matchings between vertices and triangles of corresponding trian-gulations of a punctured disc. For triangulationsâ€¦ (More)

We show that for cluster algebras associated with finite quivers without oriented cycles (with no coefficients), a seed is determined by its cluster , as conjectured by Fomin and Zelevinsky. We alsoâ€¦ (More)

This category was introduced in [1] and has been studied by Assem, BrÃ¼stle, Schiffler and Todorov [2], the authors [3], Thomas [4], Wralsen [5] and Zhu [6]. In particular, Thomas and Zhu have shownâ€¦ (More)