Abstract
We introduce the class of split Malcev Poisson algebras as the natural extension of split (noncommutative) Poisson algebras. We show that if \( P \) is a split Malcev Poisson algebra then \( P=\oplus_{j\in J}I_{j} \) with \( I_{j} \) a nonzero ideal of \( P \) such that \( \{I_{j_{1}},I_{j_{2}}\}=I_{j_{1}}I_{j_{2}}=0 \) for \( j_{1}\neq j_{2} \). Under some conditions, the above decomposition of \( P \) involves a family of the simple ideals of \( P \).
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Acknowledgment
The author thanks the referee for his review of the paper as well as for the interesting suggestions that helped to improve the work.
Funding
The author acknowledges the Fundação para a Ciência e a Tecnologia for the grant with reference SFRH/BPD/101675/2014 and the financial assistance by the Center for Mathematics of the University of Coimbra–UID/MAT/00324/2013, funded by the Portuguese Government through FCT/MEC and cofunded by the European Regional Development Fund through the Partnership Agreement PT2020. The author was also supported by the PCI of the UCA “Teoría de Lie y Teoría de Espacios de Banach,” by the PAI (Projects FQM298 and FQM7156) and by the Spanish Ministerio de Educación y Ciencia (Project MTM2013–41208P).
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Translated from Sibirskii Matematicheskii Zhurnal, 2021, Vol. 62, No. 3, pp. 633–643. https://doi.org/10.33048/smzh.2021.62.314
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Sánchez, J.M. On Split Malcev Poisson Algebras. Sib Math J 62, 511–520 (2021). https://doi.org/10.1134/S0037446621030149
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DOI: https://doi.org/10.1134/S0037446621030149