Post-Lie conformal algebra structures on Lie conformal algebras

Abstract

In this paper, we introduce and study post-Lie conformal algebras (PLCAs), a generalization of post-Lie algebras to conformal algebras. We establish an equivalence between PLCA structures and Rota-Baxter operators of weight 1 on Lie conformal algebras. We also show that every PLCA induces a new Lie conformal algebra and study PLCA structures on pairs of Lie conformal algebras. Finally, we classify all PLCA structures on two important classes of Lie conformal algebras: B(q) and W(b), achieved through Rota-Baxter operators of weight 1.