中文摘要：

利用Grbner-Shirshov基和Anick方法,构造了量子包络代数Uq（sl2）的Anick分解。作为一个应用,还讨论了Uq（sl2）的一些同调性质和Poincaré级数。

英文摘要：

By using the Grbner-Shirshov basis and the method of Anick,we construct the Anick resolution for the quantum enveloping algebra Uq （sl2）. As an application,we consider some homological properties and the Poincaré series of Uq （sl2）.