This is the first of a two-volume set that provides a modern account of the representation
theory of finite dimensional associative algebras over an algebraically closed field. The …

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 …

We investigate cluster-tilting objects (and subcategories) in triangulated 2-Calabi–Yau and
related categories. In particular, we construct a new class of such categories related to …

We provide a quiver-theoretic interpretation of certain smooth complete simplicial fans
associated to arbitrary finite root systems in recent work of S. Fomin and A. Zelevinsky. The …

Maximal green sequences are particular sequences of quiver mutations appearing in the
context of quantum dilogarithm identities and supersymmetric gauge theory. Interpreting …

We define and study virtual representation spaces for vectors having both positive and
negative dimensions at the vertices of a quiver without oriented cycles. We consider the …

Let Λ be an Artin algebra over a commutative Artin ring R and let modΛ be the category of
finitely generated left Λ-modules. For a module M∈ modΛ, we denote by pdΛ M the …

arXiv:1012.6014v1 [math.RT] 29 Dec 2010 Page 1 arXiv:1012.6014v1 [math.RT] 29 Dec 2010
TILTING THEORY AND CLUSTER ALGEBRAS IDUN REITEN Introduction The purpose of this …

Let k be an algebraically closed field and H a Hom-and Ext-finite hereditary abelian k-
category with tilting objects. It is proved that the cluster-tilting graph associated with H is …

The starting point of this thesis was a question by Dieter Happel with the following
background. Let Q be a finite acyclic quiver (another word for directed graph) and K an …