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.
作者
郭瑞芝
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)
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
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)
关键词
左右等价
Z4-不变势函数芽
分类
标准形
left-right equivalence
Z4-invariant potential function germs
classification
normal form
