Bialgebras, Manin triples of Malcev-Poisson algebras and post-Malcev-Poisson algebras

TL;DR

This paper introduces Malcev-Poisson bialgebras, explores their structural equivalences, and presents post-Malcev-Poisson algebras as new algebraic structures linked to Rota-Baxter operators.

Contribution

It defines Malcev-Poisson bialgebras, establishes their equivalences, and introduces post-Malcev-Poisson algebras as a novel structure related to Rota-Baxter operators.

Findings

Established the equivalence between matched pairs, Manin triples, and Malcev-Poisson bialgebras.

Introduced the concept of post-Malcev-Poisson algebras.

Connected post-Malcev-Poisson algebras to weighted relative Rota-Baxter operators.

Abstract

A Malcev-Poisson algebra is a Malcev algebra together with a commutative associative algebra structure related by a Leibniz rule. In this paper, we introduce the notion of Malcev-Poisson bialgebra as an analogue of a Malcev bialgebra and establish the equivalence between matched pairs, Manin triples and Malcev-Poisson bialgebras. Moreover, we introduce a new algebraic structure, called post-Malcev-Poisson algebras. Post-Malcev-Poisson algebras can be viewed as the underlying algebraic structures of weighted relative Rota-Baxter operators on Malcev-Poisson algebras.