Rota-type operators on 2-dimensional dendriform algebras

TL;DR

This paper classifies various Rota-type operators such as Rota-Baxter, Reynolds, Nijenhuis, and Averaging operators on 2-dimensional dendriform algebras over the complex numbers, expanding understanding of their algebraic structures.

Contribution

It provides a comprehensive description and classification of Rota-type operators on 2-dimensional dendriform algebras, a previously less-explored area.

Findings

Complete classification of Rota-Baxter operators on 2D dendriform algebras

Descriptions of Reynolds, Nijenhuis, and Averaging operators in the same setting

New insights into the structure of low-dimensional dendriform algebras

Abstract

We describe Rota-Baxter operators, Reynolds operators, Nijenhuis operators, and Averaging operators on 2-dimensional dendriform algebras over $\mathbb{C}$.