RETRACTED ARTICLE: Split Malcev-Poisson-Jordan algebras

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 $[I_{j_1},I_{j_2}]=I_{j_1}{I}_{j_2}=0$ for $j_1\ne j_2$. Under certain conditions, it is shown that the above decomposition of P is by means of the family of its simple ideals.

Keywords:

• Malcev-Poisson-Jordan algebras
• structure theory
• roots
• root spaces

2020 Mathematics Subject Classification:

• 17A60
• 17B22

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Statement of Retraction

Additional information

Funding

The first author was supported by the Center for Mathematics of the University of Coimbra - UIDB/00324/2020, funded by the Portuguese Government through FCT/MCTES. The second author acknowledges the support by the PCI of the UCA ‘Teoría de Lie y Teoría de Espacios de Banach’ and by the PAI with project number FQM298.