106 citations · 247 across the 24 of their papers we have counts for
9 papers · 1 filter
The image of the derived category in the cluster category
Claire Amiot, Steffen Oppermann
Cluster categories of hereditary algebras have been introduced as orbit categories of their derived categories. Keller has pointed out that for non-hereditary algebras orbit catego…
Graded mutation in cluster categories coming from hereditary categories with a tilting object
Marco Angel Bertani-Økland, Steffen Oppermann, Anette Wrålsen
We present a graded mutation rule for quivers of cluster-tilted algebras. Furthermore, we give a technique to recover a cluster-tilting object from its graded quiver in the cluster…
Algebras of acyclic cluster type: tree type and type
Claire Amiot, Steffen Oppermann
In this paper, we study algebras of global dimension at most 2 whose generalized cluster category is equivalent to the cluster category of an acyclic quiver which is either a tree…
-angulated categories
Christof Geiss, Bernhard Keller, Steffen Oppermann
We define -angulated categories by modifying the axioms of triangulated categories in a natural way. We show that Heller's parametrization of pre-triangulations extends to pre-$…
Generating the bounded derived category and perfect ghosts
Steffen Oppermann, Jan Stovicek
We show, for a wide class of abelian categories relevant in representation theory and algebraic geometry, that the bounded derived categories have no non-trivial strongly finitely…
Mutating loops and 2-cycles in 2-CY triangulated categories
Marco Angel Bertani-Økland, Steffen Oppermann
We derive an algorithm for mutating quivers of 2-CY tilted algebras that have loops and 2-cycles, under certain specific conditions. Further, we give the classification of the 2-CY…