一个特殊的4维幂零左对称代数的导子和自同构

The Derivation and Automorphism of a Special 4-dimensional Nilpotent Left-symmetric Algebra

本文对Kim Hyuk提出的一个特殊的4维幂零左对称代数L1进行了研究。通过计算线性变换作用在代数生成元上的结果,得到了幂零左对称代数L1及其相邻李代数的导子和自同构的矩阵形式,并且发现幂零左对称代数L1的导子代数是一个Able李代数,L1的相邻李代数是可完备化的。

This paper talks about L1 proposed by Kim Hyuk,which is a special 4-dimensional nilpotent left-symmetric algebra.The matrixforms of the derivation and the automorphism of L1 and its sub-adjacent Lie algebra are obtained by calculating the generators of linear transform on the algebra.It is found that the derivation algebra of L1 is a Able Lie algebra,and the sub-adjacent Lie algebraof is completable.