A non-simply laced version for cluster structures on 2-Calabi-Yau categories

TL;DR

This paper extends cluster structures to non-simply laced cases in 2-Calabi-Yau categories, showing that categories with certain cluster tilting subcategories possess generalized cluster structures, including over non-algebraically closed fields.

Contribution

It introduces a non-simply laced version of cluster structures for 2-Calabi-Yau categories, broadening the scope beyond simply-laced cases.

Findings

Categories with cluster tilting subcategories without loops or 2-cycles have generalized cluster structures.

The results apply to cluster categories over non-algebraically closed fields.

The work generalizes existing cluster theory to non-simply laced settings.

Abstract

This paper investigates a non simply-laced version of cluster structures for 2-Calabi-Yau or stably 2-Calabi-Yau categories over arbitrary fields. It results that 2-Calabi-Yau or stably 2-Calabi-Yau categories having a cluster tilting subcategory with neither loops nor 2-cycles do have the generalized version of cluster structure. This is in particular the case of cluster categories over non-algebraically closed fields.