Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (4): 769-776.

• Articles • Previous Articles     Next Articles

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

 JIN Quan-Qin, LI Xiu-Xian, TAI Zhao-Dong   

  1. Department of Mathematics, Tongji University, Shanghai 200092
  • Received:2012-09-07 Revised:2013-12-28 Online:2014-08-25 Published:2014-08-25
  • Supported by:

    国家自然科学基金(11071187)资助

Abstract:

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

Key words: Quaternions, Classical Lie algebras, MAD subalgebras, Conjugate

CLC Number: 

  • 17B05
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