Silted algebras

TL;DR

This paper characterizes algebras arising as endomorphism algebras of 2-term silting complexes in derived categories of hereditary categories, showing they are exactly the algebras of small homological dimension.

Contribution

It provides a complete characterization of such algebras, linking silting theory with homological dimensions in hereditary contexts.

Findings

Algebras of small homological dimension correspond to endomorphism algebras of 2-term silting complexes.

Module categories of these algebras appear as hearts of bounded t-structures.

The paper characterizes these algebras via their indecomposable modules' homological dimensions.

Abstract

We study endomorphism algebras of 2-term silting complexes in derived categories of hereditary finite dimensional algebras, or more generally of $\mathop{\rm Ext}\nolimits$-finite hereditary abelian categories. Module categories of such endomorphism algebras are known to occur as hearts of certain bounded $t$-structures in such derived categories. We show that the algebras occurring are exactly the algebras of small homological dimension, which are algebras characterized by the property that each indecomposable module either has injective dimension at most one, or it has projective dimension at most one.