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

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