Mutations of simple-minded systems in Calabi-Yau categories generated by a spherical object

TL;DR

This paper defines and classifies higher simple-minded systems in Calabi-Yau categories generated by spherical objects, exploring their mutations and configurations, thus extending mutation theory in cluster-tilting contexts.

Contribution

It introduces a new classification of higher simple-minded systems and studies their mutations in Calabi-Yau categories with spherical objects, providing an explicit mutation theory analogue.

Findings

Classification of higher simple-minded systems

Analysis of mutations and configurations

Extension of mutation theory in Calabi-Yau categories

Abstract

In this article, we give a definition and a classification of 'higher' simple-minded systems in triangulated categories generated by spherical objects with negative Calabi-Yau dimension. We also study mutations of this class of objects and that of 'higher' Hom-configurations and Riedtmann configurations. This gives an explicit analogue of the nice mutation theory exhibited in cluster-tilting theory.