Vertex Operator Representations Of 3-twisted Affine Lie Algebra (?)[θ] And Modules For Vertex Algebra

In this thesis, we give p-twisted affine Lie algebra. We begin with the simplest Liealgebra sl(2,(?)), then construct vertex operator representation (?) of 3-twisted a?neLie algebra (?)[θ] by Z₃-twisted vertex operators. We also prove that VQ which is an irreducible submodule VP is a vertex operatoralgebra. Furthermore, {Y (v,z) | v ∈ V_Q} is a local space spanned by untwisted vertexoperators on VP, as a result, there is a maximal local subspace containing {Y (v,z) | v ∈V_Q},which is a vertex algebra, accordingly, VP is an untwisted module for vertex algebra.There are similar results for (?).