Abstract: Defined the complex linear representation of the generalized quaternion algebras over a field K, where K is a subfield of the complex number field C. We have determind completely these representations. Using this result, we gave a necessary and sufficient condition about the problem of the isomorphism of two generalized quaternion algebras.

Key words: quaternion algebra, complex liner representation, isomorphism

摘要： 定义并完全决定了广义四元数代数的复线性表示。利用这一结果，给出了两个广义四元数代数同构的一个充分必要条件。

关键词: 四元数代数, 复线性表示, 同构