Homotopy Gerstenhaber Structures and Vertex Algebras |
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Authors: | I Gálvez V Gorbounov A Tonks |
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Institution: | 1.Universitat Autònoma de Barcelona,Bellaterra,Spain;2.University of Aberdeen,Aberdeen,UK;3.London Metropolitan University,London,UK |
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Abstract: | 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). |
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