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.

利用系数极大项，证明了这类代数是半单代数有二维交换子代数。

Moreover, the inner automorphism group of a basic quasi-hereditary algebra acts transitively on the set of its exact Borel subalgebras.

【摘要】： 正 It is proved that the exact Borel subalgebras of a basic quasi-hereditary algebra are conjugate to each other.