O - N structures on vertex operator algebras

We study Nijenhuis operators on vertex operator algebras and their connection to O-operators; this connection leads to a further exploration of O-N structures and O-dual-N structures. We prove that both an O-N structure and an O-dual-N structure can generate a series of O-operators. Conversely, under certain conditions, a pair of O-operators can also induce an O-dual-N structure.