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

Abstract

AbstractIn 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.