Poisson structures on associated with rigid Lie algebras
classification
🧮 math.RA
math-phmath.MP
keywords
poissonalgebrarigidalgebrasassociatedbracketbracketscalculus
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We present the classical Poisson-Lichnerowicz cohomology for the Poisson algebra of polynomials $\mathbb{C}[X_{1},..., X_{n}]$ using exterior calculus. After presenting some non homogeneous Poisson brackets on this algebra, we compute Poisson cohomological spaces when the Poisson structure corresponds to a bracket of a rigid Lie algebra.
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