Anti-Rota-Baxter operators on Witt and Virasoro algebras

TL;DR

This paper classifies all homogeneous anti-Rota-Baxter operators on Witt and Virasoro algebras and describes such operators on the simple Lie algebra sl_2, advancing the understanding of algebraic operator structures.

Contribution

It provides a complete description of homogeneous anti-Rota-Baxter operators on Witt, Virasoro, and sl_2 algebras, which was previously unknown.

Findings

Classified all homogeneous anti-Rota-Baxter operators on Witt and Virasoro algebras.

Described anti-Rota-Baxter operators on the simple Lie algebra sl_2.

Enhanced understanding of algebraic operator structures in Lie algebras.

Abstract

In this work, we obtain the description of all homogeneous anti-Rota-Baxter operators on Witt and Virasoro algebras. Moreover, we describe anti-Rota-Baxter operators on three-dimensional simple Lie algebra $sl_2.$