On Theory of logarithmic Poisson Cohomology
- Joseph Dongho
- Alphonse Mbah
- Shuntah Roland Yotcha
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.- Full Text:
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- DOI:10.5539/jmr.v9n4p209
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