Post-Lie conformal algebra structures on Lie conformal algebras

TL;DR

This paper introduces post-Lie conformal algebras, establishes their connection with Rota-Baxter operators, and classifies such structures on specific Lie conformal algebras, expanding the algebraic framework.

Contribution

It defines post-Lie conformal algebras, links them to Rota-Baxter operators, and classifies these structures on B(q) and W(b) Lie conformal algebras.

Findings

Post-Lie conformal algebras are equivalent to Rota-Baxter operators of weight 1.

Every PLCA induces a new Lie conformal algebra.

Complete classification of PLCA structures on B(q) and W(b).

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.