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BV-algebra strucuture on Poisson cohomology Wu, Quanshui
Description
Similar to the modular vector fields in Poisson geometry, modular derivations can be defined for smooth Poisson algebras with trivial canonical bundle. By twisting Poisson modules with the modular derivation, the Poisson cochain complex with values in any Poisson module is isomorphic to the Poisson chain complex with values in the corresponding twisted Poisson module. Then a version of twisted Poincar\'{e} duality is deduced between Poisson homologies and Poisson cohomologies. If the Poisson structure is pseudo-unimodular, then its Poisson cohomology as Gerstenhaber algebra is exact, that is, it has a Batalin-Vilkovisky algebra structure by using the isomorphism between the Poisson cochain complex and chain complex.
Item Metadata
Title |
BV-algebra strucuture on Poisson cohomology
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2016-09-13T13:30
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Description |
Similar to the modular vector fields in Poisson geometry, modular derivations can be defined for smooth Poisson
algebras with trivial canonical bundle. By twisting Poisson modules with the modular derivation, the Poisson cochain complex with values in any Poisson module is isomorphic to the Poisson chain complex with values in the corresponding twisted Poisson module. Then a version of twisted Poincar\'{e} duality is deduced between Poisson homologies and Poisson cohomologies. If the Poisson structure is pseudo-unimodular, then its Poisson cohomology as Gerstenhaber algebra is exact, that is, it has a Batalin-Vilkovisky algebra structure by using the isomorphism between the Poisson cochain complex and chain complex.
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Extent |
59 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Fudan University
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Series | |
Date Available |
2017-03-15
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0343182
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International