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Logarithmic Poisson cohomology: example of calculation and application to prequantization
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In this paper we introduce the notions of logarithmic Poisson structure and logarithmic principal Poisson structure. We prove that the latter induces a representation by logarithmic derivation of the module of logarithmic Kähler differentials. Therefore it induces a differential complex from which we derive the notion of logarithmic Poisson cohomology. We prove that Poisson cohomology and logarithmic Poisson cohomology are equal when the Poisson structure is log symplectic. We give an example of non log symplectic but logarithmic Poisson structure for which these cohomology spaces are equal. We give an example for which these cohomologies are different. We discuss and modify the K. Saito definition of logarithmic differential forms. This note ends with an application to a prequantization of the logarithmic Poisson algebra: (ℂ[x,y],{x,y}=x).
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Title: Logarithmic Poisson cohomology: example of calculation and application to prequantization
Description:
In this paper we introduce the notions of logarithmic Poisson structure and logarithmic principal Poisson structure.
We prove that the latter induces a representation by logarithmic derivation of the module of logarithmic Kähler differentials.
Therefore it induces a differential complex from which we derive the notion of logarithmic Poisson cohomology.
We prove that Poisson cohomology and logarithmic Poisson cohomology are equal when the Poisson structure is log symplectic.
We give an example of non log symplectic but logarithmic Poisson structure for which these cohomology spaces are equal.
We give an example for which these cohomologies are different.
We discuss and modify the K.
Saito definition of logarithmic differential forms.
This note ends with an application to a prequantization of the logarithmic Poisson algebra: (ℂ[x,y],{x,y}=x).
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