Applied Categorical Structures

, Volume 18, Issue 1, pp 1–15 | Cite as

Homotopy Gerstenhaber Structures and Vertex Algebras

  • I. Gálvez
  • V. Gorbounov
  • A. Tonks


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 (Trans Amer Math Soc 319:631–661, 1990).


BRST complex Homotopy Gerstenhaber algebra Vertex algebra Chiral de Rham complex 

Mathematics Subject Classifications (2000)

17B69 55S99 81T40 


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© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Universitat Autònoma de BarcelonaBellaterraSpain
  2. 2.University of AberdeenAberdeenUK
  3. 3.London Metropolitan UniversityLondonUK

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