一类无穷维李代数的自同构群

令W表示秩为1的Witt代数,是定义在除去2个固定点为正则的Riemann球面上的半纯向量场李代数,也是一个圈上多项式向量场李代数的复化及罗朗多项式环的导子李代数,在数学和物理学的很多领域中有着重要应用.设V是一个向量空间,由某种作用将其看作W-模.设G是Witt代数W由模V得到的分裂扩张.主要研究了分裂扩张G的结构,并给出了G的自同构群,所得结果丰富了李理论的内容.

Automorphism groups of a class of infinite dimensional Lie algebra

Let W denote the rank-one Witt algebra.It is the Lie algebra of meromorphic vector fields defined on the Riemann sphere that are holomorphic except the two fixed points.It is also the complexification of the Lie algebra of polynomial vector fields on a circle and the Lie algebra of derivations of the ring of Laurent polynomials,and plays an important role in many areas of Mathematics and Physics.Let V be a vector space which can be regarded as W-module due to some kind of action.Let G be the split extension of Witt algebra W obtained by its module V.The structure of G is studied,and the automorphism groups of G are given.The results enrich the contents of the Lie theory.