Generalized Vertex Operator Algebras Of Type B_n～(1),C_n～(1),F₄～(1),G₂～(1)

This thesis discusses the corresponding vertex operator algebras on the basis of professor Xu's vertex operator representation of type B_n¹, C_n¹, F₄¹, G₂¹ It is well known that root lattice vertex algebras can be used to solve the problem of constructing vertex operator algebras of type A_n¹, D_n¹, E₆¹, E₇¹, E₈¹ If we use the same method as in root lattice vertex algebras to construct vertex operator algebras of type B_n¹, C_n¹, F₄¹, G₂¹, there would be some difficulties in the computation of fractional cases. This thesis gives a formal product between vertex operators by inserting a coefficient function into the usual product of vertex operators, to solve a sequence of the above difficulties.