发表机构
Chern Institute of Mathematics & LPMC, Nankai University; Nankai University; School of Mathematics, Hangzhou Normal University（南开大学陈省身数学研究所及LPMC; 南开大学; 杭州师范大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文引入可分解Lie共形双代数，建立其与非零权二次Rota-Baxter Lie共形代数的对应，并推广至Gel'fand-Dorfman情形，诱导多种共形代数结构。
AI 中文摘要
我们引入了可分解的Lie共形双代数的概念，并建立了它们与非零权二次Rota-Baxter Lie共形代数之间的对应关系。因此，一方面，带有非零权Rota-Baxter算子的Lie共形双代数给出一个可分解的Lie共形双代数。另一方面，作为二次Rota-Baxter Lie代数诱导广义伪Hessian post-Lie代数和特殊部分预-post-Lie代数这一事实的共形类比，二次Rota-Baxter Lie共形代数以及可分解的Lie共形双代数诱导广义伪Hessian post-Lie共形代数和特殊部分预-post-Lie共形代数。此外，我们将Gel'fand-Dorfman双代数与一类Lie共形双代数之间的对应关系推广到可分解情形。不仅可分解的Gel'fand-Dorfman双代数与一类可分解的Lie共形双代数之间存在对应关系，而且它们对应的二次Rota-Baxter对应物以及若干诱导结构之间也存在对应关系。特别地，存在从带有非零权Rota-Baxter算子的Gel'fand-Dorfman双代数构造可分解的Lie共形双代数的方法。
英文摘要
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.
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