Cartan

基本解释

All finite-dimensional path lie algebras are solvable and their Cartan subalgebras of them are obtained.
给出了有限维路李代数均可解的结论和所有的卡当子代数；
The root space decompositions of them relative to specific Cartan subalgebras are given.
并给出了其相对于一个特定的卡当子代数的根子空间的分解；
Cartan domain to Hua domain II.
嘉当域到华罗庚域2。
Let A be a symmetrizable generalized Cartan matrix, g(A) thecorresponding Kac-Moody algebra, then a subalgebra h of g(A) is a split Cartan subalgebra if and only if there is a regular locally finite element x such that h=g 0(adx).
设A为一可对称化广义Cartan矩阵 ;g(A)为对应的Kac_Moody代数 ;则 g(A)的子代数h为可裂Cartan子代数的充分必要条件为存在正则局部有限元x ;使得h =g0 (adx) .
With the aborative description of geometry and analytics,applying Cartan Method,gets the Euler equation of weakly harmonic maps from high dimension Riemann manifold to homogeneous space.
借助于几何上与分析上的精细刻画;利用卡坦方法;得到高维Riemann流形到齐次空间弱调和映射体现的具体Euler方程形式.