On endomorphism algebras of silting complexes over hereditary abelian categories

Abstract

Let $\mathcal{E}$ be the class of finite-dimensional algebras isomorphic to endomorphism algebras of silting complexes over hereditary abelian categories. It is proved that the class $\mathcal{E}$ is closed under taking idempotent quotients, idempotent subalgebras and $\tau$-reduction. We also show that the proper class consisting of shod algebras is also closed under these operations. In addition, several classic classes of algebras -- including laura, glued, weakly shod algebras -- are proved to be closed under idempotent quotients, thereby generalizing a known result originally established for specific idempotents.

23 pages