Let Λ be a finite dimensional, connected, associative algebra with unit over a field k. Let n be the number of isomorphism classes of simple Λ-modules. By modΛ we denote the category of finite dimensional left Λ-modules. A module ΛT ∈ modΛ is called a tilting module if (i) the projective dimension pd ΛT of ΛT is finite, and (ii) ExtiΛ(T, T) = 0 for all i> 0, and (iii) there is an exact sequence 0 → ΛΛ → ΛT 1 → · · · → ΛT d → 0 with ΛT i ∈ add ΛT for all 1 ≤ i ≤ d. Here add ΛT denotes the category of direct sums of direct summands of ΛT. Tilting modules play an important role in many branches of mathematics such as repre-sentation theory of Artin algebras or the theory of algebraic groups. Let m⊕ i=1 Ti be the decomposition of ΛT into indecomposable direct summands. We call

J. Marsh and Idun Reiten Associated to any acyclic cluster algebra is a corresponding triangulated category known as the

Abstract. In this paper we give a direct proof of the properties of the ZD∞ category which was introduced in the classification of noetherian, hereditary categories with Serre duality by Idun Reiten and the author. 1.

Dedicated to Idun Reiten on the occasion of her seventieth birthday. Abstract. Fomin-Zelevinsky conjectured that in any cluster algebra, the cluster monomials are linearly independent and that the exchange graph is independent of the choice of coefficients. We confirm these conjectures for all skew

Abstract. We prove that the stable endomorphism algebra of a module without self-extensions over a special biserial algebra is a gentle algebra. In particular, it is again special biserial. As a consequence, any algebra which is derived equivalent to a gentle algebra is gentle. Dedicated to Idun

Dedicated to Professor Idun Reiten on the occasion of her 60-th birthday Abstract. We shall show that every stable equivalence (functor) between represen-tation-finite selfinjective algebras not of type (D3m, s/3, 1) with m ¸ 2, 3- s lifts to a standard derived equivalence. This implies that all

The authors wish to dedicate this paper to Idun Reiten on the occasion of her sixtieth birthday. Abstract. The two main theorems proved here are as follows: If A is a finite dimensional algebra over an algebraically closed field, the identity component of the algebraic group of outer automorphisms

type A. As a consequence of our classification we establish closed formulae enumerating the torsion pairs in cluster tubes, and obtain that the torsion pairs in cluster tubes exhibit a cyclic sieving phenomenon. Dedicated to Idun Reiten on the occasion of her 70th birthday. 1.

Dedicated to Professor Idun Reiten on the occasion of her seventieth birthday. We study extension spaces, cotorsion pairs and their mutations in the cluster category of a marked surface without punctures. Under the one-to-one correspondence between the curves, valued closed curves in the marked

This is the second part in a series of two lectures with Idun Reiten. We shall show that cluster tilting mutation is compatible with quiver mutation and QP mutation. Throughout let K be an algebraically closed field, and let C be a Hom-finite 2-Calabi-Yau triangulated category over K