Homotopy algebraic structures on vetrex algebras

An important result of Lian and Zuckerman says that vertex algebras of a special class, topological vertex algebras, admit a differential, whose homology is a Gerstenhaber algebra. We discuss the homotopy algebraic structures on such a vertex algebra, related to this Gertenhaber algebra on the cohomology in the inportant class of vertex algebras coming from the Chiral de Rham complex on a manifold.