Rota-type operators on null-filiform associative algebras

TL;DR

This paper classifies various linear operators such as Rota-Baxter, Reynolds, Nijenhuis, Average, and differential operators of weight 1 on null-filiform associative algebras across any dimension.

Contribution

It provides a comprehensive description and classification of these operators on null-filiform associative algebras, expanding understanding of their structure.

Findings

Explicit descriptions of homogeneous Rota-Baxter operators

Classification of Reynolds and Nijenhuis operators

Analysis of differential operators of weight 1

Abstract

We give the description of homogeneous Rota-Baxter operators, Reynolds operators, Nijenhuis operators, Average operators and differential operator of weight 1 of null-filiform associative algebras of arbitrary dimension.