5 papers
Magnitude of module categories
Erlend D. Børve, Daniel Horiatakis, Martin Kalck
We define an invariant of the module category of a representation-finite algebra by the magnitude of its Auslander algebra. This invariant will be called the magnitude of the modul…
Bricks and -tilting theory under base field extensions
Erlend D. Børve, Eric J. Hanson, Maximilian Kaipel
Let be a field extension and let be a finite-dimensional -algebra. We investigate the relationship between and with particular emphasis on…
-tilting finiteness and -tameness: Incidence algebras of posets and concealed algebras
Erlend D. Børve, Jacob Fjeld Grevstad, Endre S. Rundsveen
We prove that any -tilting finite incidence algebra of a finite poset is representation-finite, and that any -tame incidence algebra of a finite simply connected po…
Silting reduction and picture categories of 0-Auslander extriangulated categories
Erlend D. Børve
Let be an extriangulated category and let be a rigid subcategory. Generalizing Iyama--Yang silting reduction, we devise a technical…
Two-term silting and -cluster morphism categories
Erlend D. Børve
We generalise -cluster morphism categories to the setting of non-positive dg algebras with finite dimensional cohomology in all degrees. The compatibility of silting reduction…