中文摘要：

鉴于幂零李代数的结构和表示在李理论中有着重要的地位,主要讨论复数域上一类特殊的6维带参数ε的幂零李代数的代数结构.首先,在同构意义下,利用同构的定义及性质,通过大量的推导计算,确定了此类幂零李代数的自同构群同构于6阶矩阵乘法群;其次,探讨了这类幂零李代数的Centroid代数的基本性质,给出了Centroid代数的矩阵表示,同时得出这类幂零李代数的Centroid代数是一个6维幂零李代数;最后,给出了该类幂零李代数的δ-导子的矩阵表示.特别当δ为1时,探讨了该类幂零李代数的导子代数的结构,得出导子代数是10维李代数,外导子代数是5维李代数.

英文摘要：

The structure and representation of nilpotent Lie algebra play an important role in the Lie theory. The algebraic structure of a certain class of six-dimensional nilpotent Lie algebras with the parameter ε over the complex field was discussed. It is determined that in the sense of isomorphism, the automorphism group of this class of six-dimensional nilpotent Lie algebra is isomorphic to a six-order matrix multiplication group by using the definition and properties of isomorphism and a large amount of calculation. Then the properties of Centroid algebras of this class of six-dimensional nilpotent Lie algebra were analysed and its matrix representation was given. It is shown that the Centroid algebra is a six-dimensional nilpotent Lie algebra. Finally, the g-derivation of this class of six-dimensional nilpotent Lie algebras was determined. Especially in the case of δ= 1, the structure of derivation algebras was discussed and it is concluded that the derivation algebra is a ten-dimensional Lie algebra and outer derivation algebra is a five- dimensional Lie algebra.