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Post-Lie conformal algebra structures on Lie conformal algebras

Lamei Yuan, Yuhui Tan

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.

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.
Paper Structure (10 sections, 25 theorems, 128 equations)

This paper contains 10 sections, 25 theorems, 128 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Post-Lie conformal algebra structures
  4. PLCA structures on LCAs
  5. PLCA structures on pairs of LCAs
  6. Connection with Rota-Baxter operators of weight 1
  7. PLCA structures on Lie conformal algebras of Block-type
  8. PLCA structures on the Lie conformal algebras $W(b)$
  9. Rota-Baxter operators of weight 1 on $W(b)$
  10. PLCA structures on $W(b)$

Key Result

Lemma 2.5

Let $p(\lambda) = \sum\limits_{i=0}^{m} p_i \lambda^i \in \mathbb{C}[\partial,\lambda]$, $p_{i}\in\mathbb{C}[\partial]$ be a polynomial whose leading coefficient $p_m$ does not depend on $\partial$ (i.e., $p_m \in \mathbb{C}^*$). Then for any $v \in \mathbb{C}[\partial,\lambda]$, we have $\langle p(

Theorems & Definitions (68)

  • Definition 2.1
  • Definition 2.2
  • Example 2.3
  • Example 2.4
  • Lemma 2.5
  • Definition 2.6
  • Definition 2.7
  • Definition 2.8
  • Definition 2.9
  • Definition 2.10
  • ...and 58 more