Endomorphism algebras of silting complexes

TL;DR

This paper studies the structure of endomorphism algebras arising from n-term silting complexes in hereditary algebra derived categories, revealing a separated n-section in their module categories and a trisection for n=3.

Contribution

It introduces the concept of separated n-sections in module categories of endomorphism algebras of silting complexes and characterizes the case n=3 with a trisection structure.

Findings

Module categories have separated n-sections.

For n=3, a trisection structure is established.

Provides new insights into the structure of endomorphism algebras of silting complexes.

Abstract

We consider endomorphism algebras of $n$-term silting complexes in derived categories of hereditary algebras, and we show that the module category of such an endomorphism algebra has a separated $n$-section. For $n=3$ we obtain a trisection in the sense of [2].