Extended O-operators on Poisson algebras are defined and shown to be equivalent to solutions of the new extended Poisson Yang-Baxter equation, generalizing the classical O-operator characterization of Poisson Yang-Baxter solutions.
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Post-Poisson algebras, extended $\mathcal{O}$-operators and extended Poisson Yang-Baxter equations
Extended O-operators on Poisson algebras are defined and shown to be equivalent to solutions of the new extended Poisson Yang-Baxter equation, generalizing the classical O-operator characterization of Poisson Yang-Baxter solutions.