arXiv subjects

Anders S. Kortegaard

Publications and source records attributed to Anders S. Kortegaard.

3 recordsLinked to original sources

arXiv2024

Filtrations of torsion classes in proper abelian subcategories

In an abelian category $\mathscr{A}$, we can generate torsion pairs from tilting objects of projective dimension $\leq 1$. However, when we look at tilting objects of projective dimension $2$, there is no longer a natural choice of an associated torsion pair. Instead of trying to generate a torsion pair, Jensen, Madsen and Su generated a triple of extension closed classes that can filter any objects of $\mathscr{A}$. We generalize this result to proper abelian subcategories.

math.RT↗

arXiv2023

Intermediate categories for proper abelian subcategories

Let $\mathscr{A}$ be an extension closed proper abelian subcategory of a triangulated category $\mathscr{T}$, with no negative 1 and 2 extensions. From this, two functors from $Σ\mathscr{A}\ast\mathscr{A}$ to $\mathscr{A}$ can be constructed giving a snake lemma mirroring that of homology without needing a t-structure. We generalize the concept of intermediate categories, which originates from a paper by Enomoto and Saito, to the setting of proper abelian subcategories and show that under certain assumptions this collection is in bijection with torsion-free classes in $\mathscr{A}$.

math.RT↗

arXiv2022

Derived equivalences of self-injective 2-Calabi--Yau tilted algebras

Consider a $k$-linear Frobenius category $\mathscr{E}$ with a projective generator such that the corresponding stable category $\mathscr{C}$ is 2-Calabi--Yau, Hom-finite with split idempotents. Let $l,m\in\mathscr{C}$ be maximal rigid objects with self-injective endomorphism algebras. We will show that their endomorphism algebras $\mathscr{C}(l,l)$ and $\mathscr{C}(m,m)$ are derived equivalent. Furthermore we will give a description of the two-sided tilting complex which induces this derived equivalence.

math.RT↗