Homotopy Gerstenhaber structures and vertex algebras

I Gálvez; V Gorbunov; A Tonks

doi:10.1007/s10485-008-9170-3

Homotopy Gerstenhaber structures and vertex algebras

I Gálvez, V Gorbunov, A Tonks

Mathematical Science

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

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).

Original language	English
Pages (from-to)	1-15
Number of pages	15
Journal	Applied Categorical Structures
Volume	18
Issue number	1
Early online date	22 Oct 2008
DOIs	https://doi.org/10.1007/s10485-008-9170-3
Publication status	Published - Feb 2010

Keywords

BRST complex
homotopy Gerstenhaber algebra
vertex algebra
Chiral de Rham complex

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10.1007/s10485-008-9170-3

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abstract = "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). ",

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AU - Gorbunov, V

AU - Tonks, A

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AB - 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).

KW - BRST complex

KW - homotopy Gerstenhaber algebra

KW - vertex algebra

KW - Chiral de Rham complex

U2 - 10.1007/s10485-008-9170-3

DO - 10.1007/s10485-008-9170-3

M3 - Article

SN - 1572-9095

VL - 18

SP - 1

EP - 15

JO - Applied Categorical Structures

JF - Applied Categorical Structures

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ER -

Homotopy Gerstenhaber structures and vertex algebras

Abstract

Keywords

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