Universal enveloping algebras and universal derivations of Poisson algebras

@article{Umirbaev2011UniversalEA,
  title={Universal enveloping algebras and universal derivations of Poisson algebras},
  author={U. Umirbaev},
  journal={arXiv: Rings and Algebras},
  year={2011}
}
  • U. Umirbaev
  • Published 2011
  • Mathematics
  • arXiv: Rings and Algebras
Let $k$ be an arbitrary field of characteristic $0$. It is shown that for any $n\geq 1$ the universal enveloping algebras of the Poisson symplectic algebra $P_n(k)$ and the Weyl algebra $A_n(k)$ are isomorphic and the canonical isomorphism between them easily leads to the Moyal product. A basis of the universal enveloping algebra $P^e$ of a free Poisson algebra $P=k\{x_1,...,x_n\}$ is constructed and proved that the left dependency of a finite number of elements of $P^e$ over $P^e$ is… Expand
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