The Gröbner–Shirshov bases method for vertex algebras

In the paper, we show how to apply the Gröbner–Shirshov bases method for modules over an associative algebra to the study of vertex algebras defined by generators and relations. We compute Gröbner–Shirshov bases for a series of vertex algebras and study the problem of embedding of a left-symmetric algebra into a vertex one preserving the normally ordered product.