On Theory of logarithmic Poisson Cohomology

Joseph Dongho, Alphonse Mbah and Shuntah Roland Yotcha

Journal of Mathematics Research, 2017, vol. 9, issue 4, 209-230

Abstract: We define the notion of logarithmic Poisson structure along a non zero ideal $\cali$ of an associative, commutative algebra $\cal A$ and prove that each logarithmic Poisson structure induce a skew symmetric 2-form and a Lie-Rinehart structure on the $\cal A$-module $\Omega_K(\log \cali)$ of logarithmic K\"{a}hler differential. This Lie-Rinehart structure define a representation of the underline Lie algebra. Applying the machinery of Chevaley-Eilenberg and Palais, we define the notion of logarithmic Poisson cohomology which is a measure obstructions of Linear representation of the underline Lie algebra for which the grown ring act by multiplication.

Keywords: Poisson structure; Logarithmic Poisson structure; Logarithmic Poisson cohomology; Logarithmic form; Logarithmic derivation; prequantization (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:ibn:jmrjnl:v:9:y:2017:i:4:p:209-230

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