English

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

Keywords

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}
}

Comments

23 pages