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Non-associative algebras associated to Poisson algebras

Michel Goze·Elisabeth Remm
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Abstract

Poisson algebra is usually defined to be a commutative algebra together with a Lie bracket, and these operations are required to satisfy the Leibniz rule. We describe Poisson structures in terms of a single bilinear operation. This enables us to explore Poisson algebras in the realm of non-associative algebras. We study their algebraic and cohomological properties, their deformations as non-associative algebras, and give a classification in low dimensions

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Michel Goze, Elisabeth Remm. 2007-09-04. Non-associative algebras associated to Poisson algebras. https://arxiv.org/abs/math/0602246

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