SP(1,1)上伴随作用的实矩阵表示

Real Matrix Presentation of the Adjoint Action of SP(1,1)

本文用类似文献[1]的方法,先得到SP(1,1)的李代数的一组标准正交基.利用此组标准正交基建立了SP(1,1)的李代数的Cartan分解,根据具体的基和Cartan分解求出SP(1,1)的李代数的李乘积,并由此得到了SP(1,1)的李代数在李群上的伴随作用的实矩阵表示.

In this paper, we obtain a set of orthonormal bases of the SP（1,1）Lie algebras by the method of Similar Literature [1]. We then use the set to establish the Cartan decomposition of the SP（1,1）Lie algebra. Finally, according to the specific bases and the Cartan decomposition, we obtain the Lie product of the SP（1,1） Lie algebra and the real matrix presentation of the adjoint representation.