We provide a simple construction of a G∞-algebra structure on an important class of vertex algebras V, which lifts the Gerstenhaber algebra structure on BRST cohomology of V introduced by Lian and Zuckerman. We outline two applications to algebraic topology: the construction of a sheaf of G∞ algebras on a Calabi–Yau manifold M, extending the operations of multiplication and bracket of functions and vector fields on M, and of a Lie∞ structure related to the bracket of Courant
Gálvez, I.; Gorbounov, V.; Tonks, A. Homotopy Gerstenhaber structures and vertex algebras. "Applied categorical structures", 2010, vol. 18, núm. 1, p. 1-15.