某些非循环2-群模表示空间的强平坦性和平坦性（英文）  

On the properties of strong flatness and flatness of modular representation spaces for certain noncyclic 2-groups

作　　者：贾丹丹 南基洙[1] 

机构地区：[1]大连理工大学数学科学学院,大连116024

出　　处：《黑龙江大学自然科学学报》2017年第5期505-511,共7页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the National Natural Science Foundation of China(11371343)

摘　　要：研究特征为2域上,某些非循环2-群模表示空间的强平坦性和平坦性,确定对应模不变式环的深度。在阶数不为4的非循环交换2-群的不可分解表示中,有两种表示空间的类型是平坦的。对于非交换2群而言,如果群G是阶数为2^(n+2)的二面体群或广义四元数群,则其在维数为1+2~n的忠实表示都是平坦的,但都不是强平坦的。Consider the properties of strong flatness, flatness of modular representations for certain non- eyelie 2-groups over fields with characteristic 2, and determine the depth of corresponding modular invari- ant rings. Particularly, in the indecomposable representations of a noneyclic abelian 2-group of order more than four, there are two types of flat representations. For non-abelian 2-groups, if the group G is the dihedral group or the generalized quatemion group of order 2n＋2 , then its faithful representations in dimen- sion 1 ＋ 2n are flat, but not strongly flat.

关 键 词：模表示空间 非循环2-群 深度 强平坦性 平坦性 

分 类 号：O152.6[理学—数学]