广义四元数代数的Jordan中心化子和Lie中心化子

Jordan Centralizers and Lie Centralizers on Generalized Quaternion Algebras

摘要: 本文研究了实数域上广义四元数代数的Jordan中心化子和Lie中心化子，在特定条件下，证明了广义四元数代数上的每个Jordan中心化子是中心化子，同时得到了广义四元数代数的中心化子和Jordan中心化子以及Lie中心化子的矩阵表示，并且分别给出了广义四元数代数的可加映射是中心化子和Lie中心化子的等价条件。

Abstract: In this paper, we consider Jordan centralizers and Lie centralizers on generalized quaternion al-gebras over the field of real numbers. Under certain conditions, we prove that every Jordan cen-tralizer on generalized quaternion algebras is a centralizer. At the same time, we obtain the matrix representation of the centralizers and Jordan centralizers and Lie centralizers on generalized quaternion algebras, and give the equivalent conditions that additive mappings on generalized quaternion algebras are centralizers and lie centralizers respectively.