四维Novikov代数的导子代数

Derivations of Novikov algebras in dimension four

Novikov代数是一类特殊的左对称代数,与李代数的联系非常密切.导子是Novikov代数中一个非常重要的概念.主要讨论复数域上的四维Novikov代数的导子代数的结构.给出了Novikov代数以及Novikov代数的导子的定义,讨论了它们的一些简单性质及其与左对称代数的联系,找到了复数域上四维Novikov代数的分类,对于每一类四维的Novikov代数写出它在一组特定的基下的特征矩阵,利用Novikov代数的导子的定义,通过计算这类Novikov代数的导子在这组特定的基下的矩阵找出四维Novikov代数的导子的结构形式,利用表格的形式给出所有的四维Novikov代数的导子,从而得到每一类四维Novikov代数的导子代数的结构.

Novikov algebra is a special kind of left symmetric algebra ,it is closely associated with Lie algebra .Derivation is an important definition in Novikov algebra .In this paper we mainly discuss the derivations of Novikov algebras in dimension 4 .First we give the definition of Novikov algebra and its derivation ,and also discuss some basic properties of them .Second we find the classification of 4-di-mensional Novikov algebras over complex number field and give the characteristic matrices of each kind of 4-dimensional Novikov algebras .Third we compute the derivations of the Novikov algebras under a given basis according to the definition of derivation .Finally we give all the derivations of No-vikov algebras in dimension four in a table and get the derivation algebras of Novikov algebras in di-mension four .