Algebras of Jordan brackets and Generalized Poisson algebras
Ivan Kaygorodov
TL;DR
This paper constructs bases for free unital generalized Poisson superalgebras and Jordan brackets superalgebras, and proves an analogue of Farkas' Theorem for certain PI algebras, exploring relations between these algebraic structures.
Contribution
It introduces bases for these superalgebras and extends Farkas' Theorem to PI unital generalized Poisson and Jordan brackets algebras, advancing algebraic theory.
Findings
Constructed bases for free unital generalized Poisson superalgebras.
Constructed bases for free unital superalgebras of Jordan brackets.
Proved an analogue of Farkas' Theorem for PI unital generalized Poisson and Jordan brackets algebras.
Abstract
We construct a basis of free unital generalized Poisson superalgebras and a basis of free unital superalgebras of Jordan brackets. Also, we prove the analogue of Farkas' Theorem for PI unital generalized Poisson algebras and PI unital algebras of Jordan brackets. Relations beetwen generic Poisson superalgebras and superalgebras of Jordan brackets will be studied.
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