Abstract:

The authors generalized some properties of the universal enveloping algebras for Lie algebras to Leibniz algebras, and gave the definition of universal enveloping algebras U(L) of Leibniz algebras L, by means of the definition of universal enveloping algebras, obtained a set of generators f
or U(L), and determined U(L)’s uniqueness theorem and U(L)module’s structure theorem. Moreover, the existence of universal enveloping algebras  U(L) was proved.

Key words:  Leibniz algebras, universal enveloping algebras, set of generators