Algebras of Jordan brackets and Generalized Poisson 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.

Cited by in corpus (4)

• Non-associative algebraic structures: classification and structure
• Transposed Poisson structures
• On contact brackets on the tensor product
• $\frac{1}{2}$-derivations of Lie algebras and transposed Poisson algebras