A_∞型Ringel-Hall代数(英文)  

Ringel-Hall algebra of A_∞-type

作　　者：侯汝臣[1] 叶郁[1] 

机构地区：[1]中国科学技术大学数学系,安徽合肥230026

出　　处：《中国科学技术大学学报》2006年第7期712-719,共8页JUSTC

基　　金：Supported by the National Natural Science Foundation of China(10501041).

摘　　要：首先研究建立在任意域k上的A∞型路代数kA∞的有限维模范畴,给出了kA∞的有限维模范畴与A∞的有限子quiver所对应的路代数上的有限维模范畴之间的关系,特别的具体的给出了所有的不可分解有限维kA∞模,精确的刻画了不可分解模之间的模扩张;然后给定有限域k,研究了建立在有限维kA∞模范畴上的Ringel-Hall代数H(kA∞).证明了H(kA∞)恰好是当n趋向∞时H(kAn)的正向极限,特别的找到了H(kA∞)的一个PBW基,并且证明H(kA∞)恰好与它的合成子代数相符合.The category of the finite-dimensional representations of kA∞ was studied first, with all its indecomposable objects and their extenswere were given explicitly, the Ringel-Hall algebra H（kA∞） was investigated for a finite field k was investigated. The main viewpoint of this investigation is to regard H（kA∞） as the direct limit of the Ringel-Hall algebra H（kA∞）. In particular, a PBW-basis of H（kA∞） was gotten. The investigation shows that H（kA∞） coincides with its composition subalgebra.

关 键 词：箭图 路代数 量子群 RINGEL-HALL代数 正向极限 

分 类 号：O152.5[理学—数学] O153.3[理学—基础数学]