Leibniz代数的通用包络代数

摘要

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 for 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.%把李代数通用包络代数的性质推广到Leibniz代数,给出了Leibniz代数L的通用包络代数U(L)的定义,并利用该定义得到了U(L)的生成元集,确定了U(L)的唯一性定理和U(L)-模结构定理,证明了通用包络代数U(L)的存在性.