The interplay between 2-and-3-Calabi--Yau triangulated categories
arXiv:1811.07553
Abstract
This short note surveys the constructions of 3-Calabi--Yau triangulated categories with simple-minded collections due to Ginzburg and Kontsevich--Soibelman and the constructions of 2-Calabi--Yau triangulated categories with cluster-tilting objects due to Buan--Marsh--Reineke--Reiten--Todorov and Amiot, and includes a discussion on the normal form of 2-Calabi--Yau triangulated categories with cluster-tilting objects.
10 pages. The Chinese version of this survey is published in Sci. Sin. Math. with doi: 10.1360/N012018-00001