一类单李代数的自同构群

The Automorphism Group of a Class of Simple Lie Algebra

基于对一类作为单结合代数的q-量子环面的自同构和反自同构的研究,通过分析与之关联的矩阵的具体形式,得出结论:与自同构相关联的矩阵只有两类,而p≠2时不存在反自同构,p=2时与反自同构相关联的矩阵也只有两类.从而决定了这类q-量子环面的自同构和反自同构的形状,最终分别对于这两种情形,确定了与这类q-量子环面相对应的李代数的自同构群.

Based on the study on the automorphisms and anti-automorphisms of a class of simply associative q-quantum tori and analyzing the matrices related to them,a conclusion is drawn that there are only two classes of matrices related to the automorphisms,while no anti-automorphism is found when p≠2 and only two classes of matrices related to the anti-automorphisms when p=2 as well.Therefore,the automorphisms and anti-automorphisms of such a class of simply associative algebra are determined and,consequently,the automorphism group of Lie algebra related to the class of q-quantum tori is determined.