Erlend D. Børve

activity

20212026

\infty

-categories and higher extension functors

1 citations · 1 across the 9 of their papers we have counts for

collaborators

9 papers

math.RT2026

Splitting torsion classes in higher homological algebra

Erlend D. Børve, Peter Jorgensen, Mads Hustad Sandøy

Let $d ⩾ 1$ be an integer, $M$ a suitable $d$ -abelian category. There is a notion of higher torsion classes in $M$ , also known as $d$ -torsion classes. W…

math.RT2026

Picture groups and green sequences from the perspective of Ringel--Hall algebras

Erlend D. Børve

Let $k$ be an algebraically closed field and let $Λ$ be a finite-dimensional associative $k$ -algebra. We apply Joyce and Brideland's notion of Ringel--Hall algebra to prove results…

math.RT2026

$g$ -vector fans and picture categories for 0-Auslander extriangulated categories

Erlend D. Børve, Maximilian Kaipel

We extend the notion of $g$ -vector fan so that it is defined for a Hom-finite Krull-Schmidt 0-Auslander $k$ -linear extriangulated category $C$ with a projective…

math.RT2026

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…

math.RT2025

Bricks and $τ$ -tilting theory under base field extensions

Erlend D. Børve, Eric J. Hanson, Maximilian Kaipel

Let $K : k$ be a field extension and let $Λ$ be a finite-dimensional $k$ -algebra. We investigate the relationship between $Λ$ and $Λ_{K} = Λ \otimes_{k} K$ with particular emphasis on var…

math.RT2024

$τ$ -tilting finiteness and $g$ -tameness: Incidence algebras of posets and concealed algebras

Erlend D. Børve, Jacob Fjeld Grevstad, Endre S. Rundsveen

We prove that any $τ$ -tilting finite incidence algebra of a finite poset is representation-finite, and that any $g$ -tame incidence algebra of a finite simply connected pos…

math.RT2024

Silting reduction and picture categories of 0-Auslander extriangulated categories

Erlend D. Børve

Let $C$ be an extriangulated category and let $R \subseteq C$ be a rigid subcategory. Generalizing Iyama--Yang silting reduction, we devise a technical…

math.CT2021★ 1 cited

A theorem of Retakh for exact $\infty$ -categories and higher extension functors

Erlend D. Børve, Paul Trygsland

We define extension $\infty$ -categories for exact $\infty$ -categories in terms of bifibrations. Extension $\infty$ -categories are invariant when passing to the stable hull, and con…

math.RT2021

Two-term silting and $τ$ -cluster morphism categories

Erlend D. Børve

We generalise $τ$ -cluster morphism categories to the setting of non-positive dg algebras with finite dimensional cohomology in all degrees. The compatibility of silting reduction w…

Splitting torsion classes in higher homological algebra

Picture groups and green sequences from the perspective of Ringel--Hall algebras

g-vector fans and picture categories for 0-Auslander extriangulated categories

Magnitude of module categories

Bricks and τ-tilting theory under base field extensions

τ-tilting finiteness and g-tameness: Incidence algebras of posets and concealed algebras

Silting reduction and picture categories of 0-Auslander extriangulated categories

A theorem of Retakh for exact ∞-categories and higher extension functors

Two-term silting and τ-cluster morphism categories

$g$ -vector fans and picture categories for 0-Auslander extriangulated categories

Bricks and $τ$ -tilting theory under base field extensions

$τ$ -tilting finiteness and $g$ -tameness: Incidence algebras of posets and concealed algebras

A theorem of Retakh for exact $\infty$ -categories and higher extension functors

Two-term silting and $τ$ -cluster morphism categories