有限连通赋值AR-箭图的Galois覆盖

THE GALOIS COVERINGS OF FINITE CONNECTED VALUED AUSLANDERREITEN QUIVERS

证明了当Γ是有限连通的赋值ＡＲ－箭图时，存在Γ的有限Ｇａｌｏｉｓ覆盖Γ，使得Ｈ（Γ）１是整系数结合环，Ｈ（Γ）１ＺＱ是Ｌｉｅ子代数Ｌ（Γ）ＺＱ的泛包络代数且有Ｌｉｅ代数同构：Ｌ（Γ）／ＤＬ（Γ），这里，Ｈ（Γ）１是Γ的退化Ｒｉｎｇｅｌ－Ｈａｌ代数，Ｄ是相应的有限Ｇａｌｏｉｓ群．

Let Γ be a finite connected valued AuslanderReiten quiver,it is proved that there exists a finite Galois covering Γ of Γ,such that H(Γ)1 is an associative ring with integeral coefficient,H(Γ)1ZQ is the enveloping algebra of L(Γ)1ZQ,and L(Γ)/DL(Γ),where H(Γ)1 is the degenerate RingelHall algebra and D is the corresponding finite Galois group.