McKay箭图与覆盖空间  

On McKay quivers and covering spaces

作　　者：郭晋云[1] 

机构地区：[1]湘潭大学数学与计算科学学院,湘潭411105

出　　处：《中国科学：数学》2011年第5期393-402,共10页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:10671061);教育部博士点基金(批准号:200505042004)资助项目

摘　　要：本文研究在自然扩张和嵌入下特殊线性群和一般线性群的有限子群的McKay箭图间的关系.我们证明在特定条件下,一般线性群GL(m,C)的有限子群G的McKay箭图是其正规子群G∩SL(m,C)的McKay箭图的正则覆盖,而当把G嵌入SL(m+1,C)时,新的McKay箭图由在原来的McKay箭图的每一顶点加上一个由其Nakayama平移到其自身的箭向得到.作为例子,我们指出如何用这些方法得到一些有趣的McKay箭图.In this paper,we study the relationship between the McKay quivers of finite subgroups of special linear groups and of general linear groups,via natural extension and embedding.We show that under certain condition,the McKay quiver of a finite subgroup G of GL（m,C） is a regular covering of the McKay quiver of its normal subgroup G ∩ SL（m,C）,and when embedding G in a canonical way into SL（m ＋ 1,C）,the new McKay quiver is obtained by adding an arrow from the Nakayama translation of i back to i for each vertex i.We also show by examples that certain interesting McKay quivers can be obtained in these ways.

关 键 词：McKay箭图 覆盖空间 Nakayama平移 Beilinson箭图 

分 类 号：O157.5[理学—数学]