Classification Of 2-step Nilpotent Lie Algebras Of Dimension 8 With 4-dimensional Center

Classification of Lie algebras always is the important open problem, which progresses slowly since Umlauf first gave a classification of 6 dimensional Lie algebras in 1891. With lots of study, only low dimensional Lie algebras can be classified. Duiring these years, many methods were discovered. Although they are general and feasible in theory, there are imperfections. these methods, which can only give classification of Lie algebras with dimension lower than 7 , are not suitable for slightly higher dimensional Lie algebras. So many researchers turn to focus on some special characteristics such as 2-step nilpotent and fillingform Lie algebras.In view of impracticablity of these methods for slightly higher dimensional Lie algebras, we don't begin in general aspect, and use a new direct method, choose appropriate basis, construct techniquely and give result. This method, which needs only fewer knowledge tools, can simplify calculation and give a correct result. It is not general, but suitable for some slightly higher dimensional Lie algebras. It is an innovation and attemption for classification problem. And we also enrich the classification results.By this method, classification of 2-step nilpotent Lie algebras of dimension 8 with 4 dimensional center is given in this paper. We also calculate the Derivations of these Lie algebras...