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arXiv · 1502.07503

Deformations of Poisson algebras

Michael Penkava·Anne Pichereau
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Abstract

We study $\mathbb Z_2$-graded Poisson structures defined on $\mathbb Z_2$-graded commutative polynomial algebras. In small dimensional cases, we exhibit classifications of such Poisson structures, obtain the associated Poisson $\mathbb Z_2$-graded cohomology and in some cases, deformations of these Poisson brackets and $P_\infty$-algebra structures. We highlight differences and analogies between this $\mathbb Z_2$-graded context and the non graded context, by studying for example the links between Poisson cohomology and singularities.

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Michael Penkava, Anne Pichereau. 2015-02-26. Deformations of Poisson algebras. https://arxiv.org/abs/1502.07503

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