Vertex algebras associated to a class of Lie algebras of Krichever–Novikov type

In this paper, we study a class of infinite-dimensional Lie algebras generalizing the constant rr-term Krichever–Novikov type algebras. We associate vertex C((z))C((z))-algebras and their type zero modules to representations of these Lie algebras. An equivalence between the category of restricted modules for the Lie algebras and the category of type zero modules for the vertex C((z))C((z))-algebras is established.