四元数体上A型典型李代数MAD子代数的共轭性

A Conjugacy Theorem for the MAD Subalgebras of Classical Lie Algebras of Type A Over the Quarternions

证明了四元数体上n阶方阵构成的A型典型李代数的极大交换ad可对角化子代数的维数为n-1,并且共轭于迹为零的实对角矩阵构成的子代数.

In this paper, we prove that the maximal abelian ad-diagonalizable subalgebra of the classical Lie algebras of type A consisiting of n x n matrices over the quaternions always has dimension n - 1 and it is conjugated with the algebra of real diagonal matrices of trace zero