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Homotopy Gerstenhaber structures and vertex algebras. (English) Zbl 1268.17030

Summary: We provide a simple construction of a \(G_{\infty}\)-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 \(G_{\infty}\) algebras on a Calabi-Yau manifold \(M\), extending the operations of multiplication and bracket of functions and vector fields on \(M\), and of a \(\text{Lie}_{\infty}\) structure related to the bracket of T. J. Courant [Trans. Am. Math. Soc. 319, 631–661 (1990; Zbl 0850.70212].

MSC:

17B69 Vertex operators; vertex operator algebras and related structures
17B63 Poisson algebras
18D50 Operads (MSC2010)
53D18 Generalized geometries (à la Hitchin)

Citations:

Zbl 0850.70212
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References:

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