Journal of Algebra ( IF 0.8 ) Pub Date : 2021-01-14 , DOI: 10.1016/j.jalgebra.2020.12.027 Changjian Fu , Shengfei Geng
Let be a weighted projective line and the associated cluster category. It is known that can be realized as a generalized cluster category of quiver with potential. In this note, under the assumption that has at most three weights or is of tubular type, we prove that if the generalized cluster category of a Jacobi-finite non-degenerate quiver with potential shares a 2-CY tilted algebra with , then is triangle equivalent to . As a byproduct, a 2-CY tilted algebra of is determined by its quiver provided that has at most three weights. In the end, for any weighted projective line with at most three weights, we also obtain a realization of via Buan-Iyama-Reiten-Scott's construction of 2-CY categories arising from preprojective algebras.
中文翻译:
最多具有三个权重的加权投影线的聚类类别
让 成为加权投影线,并且 相关的群集类别。众所周知可以实现为具有潜力的颤动的广义簇类别。在本说明中,假设 最多具有三个权重或属于管状类型,我们证明如果广义聚类类别 势的Jacobi有限非退化颤抖 与之共享2CY倾斜代数 , 然后 三角形等于 。作为副产物,2-CY倾斜代数为 由它的颤动决定,前提是 最多具有三个权重。最后,对于任何加权投影线 最多包含三个权重,我们还获得了 通过Buan-Iyama-Reiten-Scott构造了由前投影代数引起的2-CY类。