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Splittings of operations for Lie-Poisson triple systems and related algebraic structures

Article scientifique 2024 Anglais

Résumé

Abstract A Lie-Poisson triple system is a Lie triple system together with a commutative associative algebra structure related by a Leibniz rule. In this paper, we study representations theory and O-operators of Lie-Poisson triple systems. We show that a representation of a Lie-Poisson triple system has a dual representation under an additional condition. Next, we introduce a new algebraic structures corresponding to the splittings of operations of Malcev-Poisson algebras and Lie-Poisson triple systems called pre-Malcev-Poisson algebras and pre-Lie-Poisson triple systems in terms of representations and O-operators. In fact, we exhibit connections between (pre-)Poisson algebras, (pre-)Malcev-Poisson algebras and (pre-)Lie-Poisson triple systems. MSC (2010): 17A40; 17A36; 17B10; 17B63; 17B38.

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Hassine, A., Chtioui, T., Mabrouk, S., Zouidi, F. (2024). Splittings of operations for Lie-Poisson triple systems and related algebraic structures. https://doi.org/10.21203/rs.3.rs-3922268/v1

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Auteur(s)

Abdelkader Ben Hassine Taoufik Chtioui Sami Mabrouk Fatma Zouidi

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