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

We investigate 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.