同无限二面体群关联的晶体群的分类(英文)

Classification of Crystallographic Groups Associated with the Infinite Dihedral Group

英文关键词:crystallographic groups  infinite dihedral group.

中文摘要:

      设Ｖ是实数域Ｒ｝上的一个２－维向量空间，Ｖ带有一个仿射的或不定的对称双线性型．无限二面体群Ｗ能够被看作ＧＬ（Ｖ）的一个子群．在本文中，在仿射群Ａ（Ｖ）中共轭的意义下将分类同Ｗ关联的所有晶体群．

英文摘要:

      Let V be a 2-dimensional vector space over the real field R with an affine or indefinite symmetric bilinear form. The infinite dihedral group W can be viewed as a subgroup of GL(V). In the present paper we will classify all crystallographic groups associated with W up to conjugation in the affine group A(V).