Split Malcev-Poisson-Jordan algebras

Elisabete Barreiro; Jose M Sanchez

paper

Split Malcev-Poisson-Jordan algebras

arXiv:2206.05547

Abstract

We introduce the class of split Malcev-Poisson-Jordan algebras as the natural extension of the one of split Malcev Poisson algebras, and therefore split (non-commutative) Poisson algebras. We show that a split Malcev-Poisson-Jordan algebra $P$ can be written as a direct sum $P = \oplus_{j \in J} I_{j}$ with any $I_{j}$ a non-zero ideal of $P$ in such a way that satisfies $[I_{j_{1}}, I_{j_{2}}] = I_{j_{1}} \circ I_{j_{2}} = 0$ for $j_{1} \neq = j_{2} .$ Under certain conditions, it is shown that the above decomposition of $P$ is by means of the family of its simple ideals.