TL;DR
This paper constructs free Poisson algebras equipped with Rota-Baxter and Nijenhuis operators, expanding algebraic structures with new operator-based frameworks.
Contribution
It introduces a method to build free Poisson algebras with Rota-Baxter and Nijenhuis operators, providing new algebraic tools.
Findings
Constructed free Poisson algebra with Rota-Baxter operator
Extended construction to Nijenhuis operator
Provides foundational algebraic structures for further research
Abstract
We construct a free Poisson algebra endowed with a Rota-Baxter operator. The same construction works for a free Poisson algebra endowed with a Nijenhuis operator.
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