保双线性型群的结构

Space of Invariant bilinear forms under representation of a group of order 8

Let G be a group of order 8 and F an algebraically closed field with char= 2. In this paper we compute the number of n degree representations of G and subsequent dimensions of the corresponding spaces of invatiant bilinear forms over the field F. We explicitly discuss about the existence of non-degenerate invariant bilinear forms.

Invariant bilinear forms under the rigid motions of a regular polygon

In this paper, for n a positve integer, we compute the number of n degree representations for a dihedral group G of order 2m, m \geq 3 and the dimensions of the corresponding spaces of G invariant bilinear forms over a complex field C. We explicitly discuss about the existence of a non-degenerate invariant bilinear form. The results are important due to their applications in the studies of physical sciences.

特征二中对角化对称双线性形式的 Hodge 算子与等距群

Hodge operators and groups of isometries of diagonalizable symmetric bilinear forms in characteristic two

本文研究了特征二向量空间上非交错对称双线性形式的等距群及其在外幂上的作用，将其视为 Hodge 算子生成代数上的模。

对于对称双线性形式的自同构的同调稳定性

Homological stability for automorphisms of symmetric bilinear forms

本文研究了对称双线性形式的自同构的同调稳定性，结合Grothendieck-Witt理论计算，确定了奇正交群在低度数中的稳定上同调结构。