在左右等价下余维数不大于3的Z_4-不变势函数芽的分类  

Classification of Z_4-invariant potential function germs under the left-right equivalence groups up to codimension 3

作　　者：郭瑞芝[1] 胡亮新 周格 GUO Rui-zhi;HU Liang-xin;ZHOU Ge(College of Mathematics and Computer Science,Hunan Normal University,Changsha 410081,China)

机构地区：[1]湖南师范大学数学与计算机科学学院,湖南长沙410081

出　　处：《高校应用数学学报（A辑）》2018年第3期253-264,共12页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(10971060)

摘　　要：以紧致Lie群Z_4为对称群,讨论在左右等价群下Z_4-不变势函数芽的分类问题.分别给出了Z_4和D_4-不变函数芽环的Hilbert基,得到了Z_4-不变函数芽环可以看成是D_4-不变函数芽环上的有限生成模的结论.通过将D_4-不变函数芽环复化,将Z_4-等变映射芽模看成该复化环上的有限生成模.因此将Z_4-不变势函数芽的分类问题转化成D_4-不变函数芽环上的有限生成模的讨论.给出了一定非退化条件下余维数不大于3的Z_4-不变函数芽的分类,并得到了相应的标准形式.In this paper,the classification of Z4-invariant potential function germs is discussed under the left-right equivalence group with the compact Lie group Z4 as a symmetry group.Hilbert bases of Z4-and D4-invariant function rings are given respectively and the conclusion that the Z4-invariant function germ ring is a finitely originated model on the ring of D4-invariant function germs is gotten.By complexification of the ring of D4-invariant function germs,Z4-equivariant mapping germs model is considered as a finitely generated model on the complexificated ring.Thus the classification of Z4-invariant potential function germs is changed into discussion on a finitely generating model on D4-invariant function germs ring.Therefore the classification of Z4-invariant function germs under some non-degenerate condition up to codimension 3 is given and the related normal forms are gotten.

关 键 词：左右等价 Z4-不变势函数芽 分类 标准形 

分 类 号：O189.1[理学—数学] O177.91[理学—基础数学]