Split Malcev-Poisson-Jordan algebras

2022/06/11 by Barreiro, Elisabete, Sanchez, Jose M
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/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 = ⊕_{j ∈ J}I_j with any I_j a non-zero ideal of P in such a way that satisfies [I_j1,I_j2] = I_j1 ∘ I_j2 = 0 for j₁ ≠ j₂. Under certain conditions, it is shown that the above decomposition of P is by means of the family of its simple ideals.

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