Non-associative algebras associated to Poisson algebras
Rings and Algebras
2007-09-04 v3 Differential Geometry
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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Cite
@article{arxiv.math/0602246,
title = {Non-associative algebras associated to Poisson algebras},
author = {Michel Goze and Elisabeth Remm},
journal= {arXiv preprint arXiv:math/0602246},
year = {2007}
}
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23 pages