Endomorphism algebras arising from mutations

TL;DR

This paper studies the structure of endomorphism algebras generated through silting and tilting mutations in derived and module categories of finite dimensional algebras, revealing new algebraic properties.

Contribution

It introduces a detailed analysis of endomorphism algebras from mutations, expanding understanding of their structural characteristics in derived and module categories.

Findings

Characterization of endomorphism algebras from silting mutations

Analysis of endomorphism algebras from tilting mutations

New structural properties identified for these endomorphism algebras

Abstract

Let $A$ be a finite dimensional algebra over an algebraically closed field $k$, $\mathcal {D}^b(A)$ be the bounded derived category of $A$-mod and $A^{(m)}$ be the $m$-replicated algebra of $A$. In this paper, we investigate the structure properties of endomorphism algebras arising from silting mutation in $\mathcal {D}^b(A)$ and tilting mutation in $A^{(m)}$-mod.