Silted algebras

We study endomorphism algebras of 2-term silting complexes in derived categories of hereditary finite dimensional algebras, or more generally of $\mathop{\rm Ext}\nolimits$-finite hereditary abelian categories. Module categories of such endomorphism algebras are known to occur as hearts of certain bounded $t$-structures in such derived categories. We show that the algebras occurring are exactly the algebras of small homological dimension, which are algebras characterized by the property that each indecomposable module either has injective dimension at most one, or it has projective dimension at most one.Comment: Fix some typos, to appear in Adv. Mat

From triangulated categories to module categories via localisation II: Calculus of fractions

We show that the quotient of a Hom-finite triangulated category C by the kernel of the functor Hom(T, -), where T is a rigid object, is preabelian. We further show that the class of regular morphisms in the quotient admit a calculus of left and right fractions. It follows that the Gabriel-Zisman localisation of the quotient at the class of regular morphisms is abelian. We show that it is equivalent to the category of finite dimensional modules over the endomorphism algebra of T in C.Comment: 21 pages; no separate figures. Minor changes. To appear in Journal of the London Mathematical Society (published version is different

Derived equivalence classification for cluster-tilted algebras of type AnA_n

In this paper we give the derived equivalence classification of cluster-tilted algebras of type An. We show that the bounded derived category of such an algebra depends only on the number of 3-cycles in the quiver of the algebra.Comment: 13 pages. New version under a new name. References have been added, and some proofs have been written out in more detai