Factorizable Lie conformal bialgebras, quadratic Rota-Baxter Lie conformal algebras and some induced structures

Abstract

We introduce the notion of factorizable Lie conformal bialgebras and establish their correspondence with quadratic Rota-Baxter Lie conformal algebras of nonzero weight. Consequently, on the one hand, a Lie conformal bialgebra with a Rota-Baxter operator of nonzero weight gives a factorizable Lie conformal bialgebra. And on the other hand, as the conformal analogue of the fact that a quadratic Rota-Baxter Lie algebra induces a generalized pseudo-Hessian post-Lie algebra and a special partial-pre-post-Lie algebra, a quadratic Rota-Baxter Lie conformal algebra as well as a factorizable Lie conformal bialgebra induces a generalized pseudo-Hessian post-Lie conformal algebra and a special partial-pre-post-Lie conformal algebra. Furthermore, we generalize the correspondence between Gel'fand-Dorfman bialgebras and a class of Lie conformal bialgebras to the factorizable cases. There is not only a correspondence between factorizable Gel'fand-Dorfman bialgebras and a class of factorizable Lie conformal bialgebras, but also a correspondence for their corresponding quadratic Rota-Baxter counterparts as well as some induced structures. In particular, there is a construction of factorizable Lie conformal bialgebras from Gel'fand-Dorfman bialgebras with a Rota-Baxter operator of nonzero weight.