Poisson algebras in terms of non-associative algebras

By Michel Goze, Elisabeth Remm. 2008

47 citations recorded by the source corpus.

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 settle the classification problem in low dimensions.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0a11e5c1c00bc8a56d67b7aa93bbbdd045872260