Admissible Poisson bialgebras

An admissible Poisson algebra (or briefly, an adm-Poisson algebra) gives equivalent presentation with only one operation for a algebra. We establish bialgebra theory algebras independently and systematically, including but beyond the corresponding results on bialgebras given in [27]. Explicitly, we introduce notion of which are to Manin triples as well bialgebras. The direct correspondence between comultiplication cocommutative anti-cocommutative comultiplications generalizes illustrates polarization–depolarization process context study special class include known coboundary [27] proper subclass general, illustrating advantage terms operation, leads introduction Yang–Baxter equation It is unexpected consequence that both associative have same form thus it motivates simplifies involved from equation, another operation. A skew-symmetric solution bialgebra. Finally, notions [Formula: see text]-operator pre-adm-Poisson introduced construct solutions hence Note pre-Poisson by Aguiar.