Graded anti-pre-Lie algebraic structures on Witt and Virasoro algebras

TL;DR

This paper classifies graded anti-pre-Lie algebraic structures on Witt algebras and shows their non-existence on Virasoro algebras under certain conditions, advancing understanding of algebraic structures in mathematical physics.

Contribution

It provides a classification of graded anti-pre-Lie structures on Witt algebras and proves their non-existence on Virasoro algebras under natural assumptions.

Findings

Classified indecomposable weight representations of Witt algebra

Established isomorphism classes of these algebraic structures

Proved non-existence of such structures on Virasoro algebra under natural conditions

Abstract

We give the graded anti-pre-Lie algebraic structures on the Witt algebra $\mathcal W$ by the classification of certain indecomposable weight representations of $\mathcal W$. Their classification in the sense of isomorphism is also given. Furthermore, there does not exist a graded anti-pre-Lie algebraic structure on the Virasoro algebra $\mathcal V$ satisfying some natural conditions.