Chinese Quarterly Journal of Mathematics ›› 2007, Vol. 22 ›› Issue (4): 482-491.

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Additive Rank-1 Preservers Between Hermitian Matrix Spaces Over Quaternion Division Algebra

  

  1. 1.Department of Mathematics, Tianjin University of Finance and Economics, Tianjin 300222, China; 2.Department of Mathematics, Harbin Institute of Technology, Harbin 150001,China
  • Received:2006-09-18 Online:2007-12-30 Published:2023-10-18
  • About author: HAN Jing-wen(1980-), female, native of Hengshui, Hebei, an assistant of Tianjin University of Finance and Economics, engaged in classical groupe and matrix algebra; ZHENG Bao-dong(1960-), male, native of Harbin, Heilongjiang, a professor of Harbin Institute of Technology, engaged in classical groups and its application.
  • Supported by:
    Supported by NSF of China(10571033)

Abstract: Let Q be the quaternion division algebra over real field F. Denote by Hn(Q)the set of all n×n hermitian matrices over Q. We characterize the additive maps from Hn(Q) into Hm(Q)that preserve rank-1 matrices when the rank of the image of In is equal to n. Let QR be the quaternion division algebra over the field of real number R. The additive maps from Hn(QR) into Hm(QR)that preserve rank-1 matrices are also given. 

Key words: additive map, quaternion division algebra, Hermitian matrix, rank

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