某些非循环2-群模表示空间的强平坦性和平坦性（英文）
发布时间：2018-08-11 12:50
【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。
[Abstract]:In this paper, we study the strong flatness and flatness of some aperiodic 2-group modules representing spaces over 2 fields, and determine the depth of corresponding modular invariant rings. In the indecomposable representations of non-cyclic commutative 2-groups of order 4, two types of representation spaces are flat. For a noncommutative 2 group, if G is a dihedral group of order 2 ~ (n 2) or a generalized quaternion group, then the faithful representation of the group G with dimension 1 2 n is flat but not strongly flat.
【作者单位】： 大连理工大学数学科学学院;
【基金】：Supported by the National Natural Science Foundation of China(11371343)
【分类号】：O152
本文编号：2177043
[Abstract]:In this paper, we study the strong flatness and flatness of some aperiodic 2-group modules representing spaces over 2 fields, and determine the depth of corresponding modular invariant rings. In the indecomposable representations of non-cyclic commutative 2-groups of order 4, two types of representation spaces are flat. For a noncommutative 2 group, if G is a dihedral group of order 2 ~ (n 2) or a generalized quaternion group, then the faithful representation of the group G with dimension 1 2 n is flat but not strongly flat.
【作者单位】： 大连理工大学数学科学学院;
【基金】：Supported by the National Natural Science Foundation of China(11371343)
【分类号】：O152
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