Using the notion of coefficient matrix and maximal element.We prove that the Lie algebra is semi-simple and it has no abelian two dimensional subalgebra.
利用系数矩阵和极大项，证明了这类李代数是半单李代数且没有二维交换子代数。
Maximal element
英语例句库
中文百科
极大元
设
是偏序集，
，
，若对于所有的
，
，则称
为
的极大元。
请注意极大元和最大元的区别。最大元是中最大的元素，它与中其它元素都可比；而极大元不一定与中其它元素都可比，只要没有比它大的元素，它就是极大元。对于有穷集合，极大元一定存在，但最大元不一定存在。最大元如果存在一定是唯一的，但极大元可能有多个。
英语百科
Maximal element 极大元
In mathematics, especially in order theory, a maximal element of a subset S of some partially ordered set (poset) is an element of S that is not smaller than any other element in S. A minimal element of a subset S of some partially ordered set is defined dually as an element of S that is not greater than any other element in S.
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