Some Research On Complete Leibniz Algebras

Complete Lie algebras and Leibniz algebras are two important kinds of algebras in Lie theory. In this artical we define a kind of new algebras—complete Leibniz algebras after summarizing pioneers' work. First of all, we discuss the properties of complete Leibniz algebras. Then we not only give the complete classification of complete Leibniz algebras of dimension less than five, but also discuss one special case of five dimension. As for the general case, we discuss the impossibility of realization of some construction method. Apart from this, we also discuss the center and the derivation algebras of complete Leibniz algebras.