n维Mbius变换的正则性  

Regularity of n Dimensional Mbius Transformations

作　　者：王仙桃[1] 蒋月评[1] 

机构地区：[1]湖南大学应用数学系,湖南长沙410082

出　　处：《数学学报（中文版）》2000年第2期309-316,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金!19801011;湖南省科学基金!98JJY2072

摘　　要：本文利用高维Ｍｂｉｕｓ变换的 Ｃｌｉｆｆｏｒｄ矩阵表示，讨论了高维 Ｍｂｉｕｓ变换的正则性；证明了三维抛物Ｍｂｉｕｓ变换一定是正则的，得到了三维非抛物Ｍｂｉｕｓ变换是正则的一条充要条件；同时举例说明上述充要条件在ＳＬ（２，　ｎ）（ｎ＝２ｋ，ｋ≥２）中不成立．In this paper, by using the Clifford matrix representation of higher dimensional Mobius transformations, we discuss the regularity of n dimensional Mobius transformations. We prove that each three dimensional parabolic Mobius transformation is regular. Also we obtain a necessary and sufficient condition for three dimensional nonparabolic Mobius transformations to be regular. In the end, we construct an example to show that the above necessary and sufficient condition does not hold in SL(2, n ) when n = 2k, k 2.

关 键 词：CLIFFORD矩阵 正慢性 抛物元素 灭比乌斯变换 

分 类 号：O174.51[理学—数学] O151.24[理学—基础数学]