Direct Product Local Vertex Lie Algebras And Some Considerations Of Local Vertex Loop-Lie Algebras

During the research of vertex (operator) algebras, conceptions of direct product and tensor product vertex algebras have been introduced. And we truly obtain new kinds of vertex algebras by those conceptions. Here, we introduce parallel conceptions in local vertex Lie algebras. And in chapter 5, we give out specific examples of direct product local vertex Lie algebras.From a Lie algebra L, we could get its loop-algebra, by which we furthermore obtain local vertex Lie algebra. By analyzing examples of such local vertex Lie algebras, we try to find a relationship——the relationship between the ideals of Lie algebra L and the vertex sub-algebras of the corresponding vertex algebra V(L), which comes from local vertex Lie algebra with Lie algebra component the loop Lie algebra of L. And we hope that this kind of relationship would help us with the research of local vertex Lie algebras' ideals.