Quasi-triangular Novikov-Poisson bialgebras and affinization of Novikov-Poisson bialgebras

We introduce the notion of quasi-triangular Novikov-Poisson bialgebras, which constructed from solutions of the Novikov-Poisson Yang-Baxter equation whose symmetric parts are invariant. A factorizable Novikov-Poisson bialgebra is a special quasi-triangular Novikov-Poisson bialgebra, and induces a factorization of the underlying Novikov-Poisson algebra. The double of any Novikov-Poisson bialgebra naturally admits a factorizable Novikov-Poisson bialgebra structure. Moreover, we show that there is a one-to-one correspondence between factorizable Novikov-Poisson bialgebras and quadratic Rota-Baxter Novikov-Poisson algebras of nonzero weights. Finally, we construct infinite-dimensional Novikov-Poisson bialgebras from finite-dimensional Novikov-Poisson bialgebras by the completed tensor product.