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

Coelho Guardado Simoes, Raquel (2017) Mutations of simple-minded systems in Calabi-Yau categories generated by a spherical object. Forum Mathematicum, 29 (5). pp. 1065-1081. ISSN 0933-7741

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.