Representations of deformed preprojective algebras and quantum groups  

作　　者：YANG ShiLin LIU JianZhen 

机构地区：[1]Department of Applied Mathematics,Beijing University of Technology,Beijing 100024,China

出　　处：《Science China Mathematics》2009年第1期109-118,共10页中国科学：数学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos. 10671016, 10771014);the Beijing Natural Science Foundation (Grant No. 1062003);Science and Technology Program of Beijing Education Committee (Grant No. KM200710005013)

摘　　要：Let (Г, I) be the bound quiver of a cyclic quiver whose vertices correspond to the Abelian group ? d . In this paper, we list all indecomposable representations of (θ, I) and give the conditions that those representations of them can be extended to representations of deformed preprojective algebra Пλ(Г, I). It is shown that those representations given by extending indecomposable representations of (Г, I) are all simple representations of Пλ(Г, I). Therefore, it is concluded that all simple representations of restricted quantum group ū q (sl 2) are realized in terms of deformed preprojective algebra.Let (Γ,I) be the bound quiver of a cyclic quiver whose vertices correspond to the Abelian group Zd. In this paper, we list all indecomposable representations of (Γ,I) and give the conditions that those representations of them can be extended to representations of deformed preprojective algebra Πλ(Γ,I). It is shown that those representations given by extending indecomposable representations of (Γ,I) are all simple representations of Πλ(Γ,I). Therefore, it is concluded that all simple representa-tions of restricted quantum group Uq(sl2) are realized in terms of deformed preprojective algebra.

关 键 词：preprojective algebra quantum group indecomposable representation 16G20 17B35 

分 类 号：O152.5[理学—数学]