3-李代数在数学及数学物理的很多领域有着广泛的应用,利用李代数实现3-李代数,一直是人们关注的问题,文章主要研究利用度量李代数的维数扩张实现3-李代数.利用m-维度量李代数V及V上的线性函数f,分别做V的一维扩张与二维扩张,构造了(m+1)-维3-李代数与(m+2)-维3-李代数,并研究了3-李代数的度量结构.
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