李共形代数与共形模

Conformal Algebras and Conformal Modules

探讨了李共形代数和形式分布李代数两者之间的关系。从而可由形式分布李代数(g,F)得到李共形代数Conf(g,F);反之,可由李共形代数A得到形式分布李代数(LieA,A)。此外,通过对李共形代数A的共形模M作用,构造了相应李代数LieA的模V(M),为李共形代数的表示论在研究无限维李代数的表示论中的运用奠定了基础。同时对Virasoro共形代数在C[坠]上自由且秩为1的共形模进行了分类。

The relationship between Lie conformal algebras and formal distribution Lie algebras was discussed in detail.Then a Lie conformal algebra Conf（g,F）could be obtained by being given a formal distribution Lie algebra（g,F）.Conversely,a formal distribution Lie algebra（LieA,A） could be obtained from a Lie conformal algebra A.Furthermore,a module V（M） of Lie algebra LieA could be obtained from a Lie conformal algebra A and a conformal A-module M.It laid the foundation for application of the representation theory of Lie conformal algebra in the representation theory of infinite dimension Lie algebra.The classification of rank 1 free conformal module of Virasoro conformal algebras was obtained.