Graded anti-pre-Lie algebraic structures on Witt and Virasoro algebras
Chengming Bai, Dongfang Gao

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 by the classification of certain indecomposable weight representations of . 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 satisfying some natural conditions.
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