Author

Erlend D. Børve

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Preprint Sep 2026

Splitting torsion classes in higher homological algebra

Let $d \geqslant 1$ be an integer, $\mathscr{M}$ a suitable $d$-abelian category. There is a notion of higher torsion classes in $\mathscr{M}$, also known as $d$-torsion classes. We generalise a classic theorem of Hoshino by providing criteria for a $d$-torsion class $\mathscr{U}$ to be splitting, notably that $\mathsc...

Erlend D. Børve, Peter Jørgensen, M. Sandøy · 0 citations

Preprint Aug 2026

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

Let $k$ be an algebraically closed field and let $\Lambda$ be a finite-dimensional associative $k$-algebra. We apply Joyce and Brideland's notion of Ringel--Hall algebra to prove results about picture spaces and picture groups. For instance, we construct a faithful group functor for $\Lambda$, i.e. a faithful functor f...

Erlend D. Børve · 1 citation