Affine Vertex Operator Algebra

In this paper,A concrete construction of Affine vertex operator algebra V（k,0）is given.By using the properties of integrable highest weight module over Kac-Moody algebras,a description of unique maximal submodule I（k,0）is given and the Zhu’s algebra of simple affine vertex operator algebra L（k,0）= V（k,0）/I（k,0）is calculated.For simple vertex operator algebra L（k,0）,by using Zhu’s A（V）theory,we give a classification of its irreducible modules when level k is positive integer.Finally,the rationality and C2-cofinite properties of L（k,0）are also given.Finally,we give another approach to the classification by using the vertex representation of s（?）₂.