We provide a simple construction of a G ¿8¿-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 ¿8¿ 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¿8¿ structure related to the bracket of Courant (Trans Amer Math Soc 319:631–661, 1990).
- BRST complex
- homotopy Gerstenhaber algebra
- vertex algebra
- Chiral de Rham complex