1.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,证明了这类李数是半单李数且没有二子数。
2.Moreover, the inner automorphism group of a basic quasi-hereditary algebra acts transitively on the set of its exact Borel subalgebras.
【】: It is proved that the exact Borel subalgebras of a basic quasi-hereditary algebra are conjugate to each other.