单李代数(simple Lie algebra)是一类结构简单的李代数。设L为域F上的李代数,若L的非零理想只有L本身,且[L,L]≠0,则L称为单李代数。单李代数必为半单李代数,反之,在实数及复数的情形,半单李代数必为单理想子代数的直和,因此,研究实及复半单李代数的问题化为研究实及复单李代数。 单李代数的命名来源于挪威数学家Sophus Lie。
... 单类估计 single-class estimation 单李代数 simple Lie algebra 单李环 simple Lie ring ...
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复半单李代数 [数] Complex semisimple lie algebras
实单李代数 [数] real simple Lie algebra
例外复单李代数 [数] exceptional complex simple Lie algebra
半单李代数 semi-simple Lie algebra
典型复单李代数 [数] classical complex simple Lie algebra
复单李代数 [数] complex simple lie algebra
典型实单李代数 classical real simple Lie algebras
半单李代数的上同调 cohomology of semi-simple Lie algebras
非紧实单纯李代数 [数] noncompact real simple Lie algebras
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在适当地选取了半单李代数的根系之后,就可算出初等表示权的标积。
When the set of roots for a semi-simple Lie algebra have been selected appropriately, the scalar product of the weights of the elementary representation can be calculated.
结果表明代数动力学方法对于具有非半单李代数结构的线性动力系统仍然适用。
It has also been shown that the algebraic dynamics might be generalized from the linear dynamic system with a semi-simple Lie algebra to that with a general Lie algebra.
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。
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.
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