星形箭图偏周期预投射代数的Hilbert级数

Partial Period Preprojective Algebra's Hilbert Series of Star Quiver

设△是一个有限无圈的箭图．引入了由△所决定的偏周期预投射代数，它是一个定义在周期为p的稳定平移箭图Z△／（τp）上的代数，记为∏Q（△，p），J．当周期P=1时，偏周期预投射代数就是偏预投射代数．我们推广了Eting和Eu的方法并得到无圈的星形箭图△所决定的偏周期预投射代数∏（Q（△，p）），J的Hilbert级数的计算公式．

Let A be a finite quiver without cycle. This paper introduces the concept of partial period preprojective algebra defined over A,which is a algebra defined on stable translation quiver Z△/（τp） of period p, denoted by ∏Q（△,p））j.when p = 1,partial period preprojective algebra is just partial preprojeetive algebra.We generalize Eting and Eu＇s way and obtain the formula of the Hilbert series of partial period preprojective algebra ∏Q（△,p））,j decided by a star quiver △ .