solvable algebra

Firstly, we prove three equivalent conditions for a solvable n-Lie algebra. Subsequently, mimicking the Borel subalgebra theory of Lie algebras, we give the definition of a Borel n-subalgebra of an n-Lie algebra, and prove two propositions about it.

第三节，证明了可解n-李代数的三个等价条件，并仿照李代数理论中的Borel子代数的定义，给出了Borel n-子代数的定义及相关性质。

We completely determined the structure of Derg of the 3-solvable non-degenerate Lie Algebra, g.

进而给出了三次可解型非退化李代数的一个等价条件，并且详细地刻画了它的导子李代数的结构。

In this paper, the Riemann-Hilbert boundary value problem for a class of first order hyperbolic equation in commutative quaternion algebra is considered, and the general solutions and the solvable conditions of the problem in different cases are obtained.

讨论了可换四元数代数中一类一阶双曲方程的Riemann-Hilbert边值问题.获得了其解的一般形式，以及在不同情况下Riemann-Hilbert边值问题的可解条件。