Algebras of Jordan brackets and generalized Poisson algebras

Abstract

We construct bases for free unital generalized Poisson superalgebras and for free unital superalgebras of Jordan brackets. Also, we prove an analogue of Farkas’ theorem for PI unital generalized Poisson algebras and PI unital algebras of Jordan brackets. Relations between generic Poisson superalgebras and superalgebras of Jordan brackets are studied.

Keywords:

• Poisson algebra
• identity
• algebra of Jordan brackets

AMS Subject Classifications:

• 17C70
• 17B01
• 17B63

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The author was supported by RFBR [15-31-21169] and by FAPESP [14/24519-8].