Rota-Type Operators on 2-Dimensional Pre-Lie Algebras

Abstract: This paper studies Rota-Baxter, Reynolds, Nijenhuis, and Averaging operators on 2-dimensional pre-Lie algebras over $\mathbb{C}$. Using the classification of 2-dimensional pre-Lie algebras and computational tools like Mathematica or Maple, we describe these Rota-type operators in detail. Our results provide a deeper understanding of these operators and their roles in algebraic structures.