4 papers · 1 filter
Maximal green sequences for string algebras
Alexander Garver, Khrystyna Serhiyenko
Maximal green sequences are important objects in representation theory, cluster algebras, and string theory. The two fundamental questions about maximal green sequences are whether…
Modules over cluster-tilted algebras that do not lie on local slices
Ibrahim Assem, Ralf Schiffler, Khrystyna Serhiyenko
We characterize the indecomposable transjective modules over an arbitrary cluster-tilted algebra that do not lie on a local slice, and we provide a sharp upper bound for the number…
Cluster-tilted and quasi-tilted algebras
Ibrahim Assem, Ralf Schiffler, Khrystyna Serhiyenko
In this paper, we prove that relation-extensions of quasi-tilted algebras are 2-Calabi-Yau tilted. With the objective of describing the module category of a cluster-tilted algebra…
Injective Presentations of Induced Modules over Cluster-Tilted Algebras
Ralf Schiffler, Khrystyna Serhiyenko
Every cluster-tilted algebra is the relation extension of a tilted algebra . A -module is called induced if it is of the form $M\otimes_C…