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

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.

18 pages

References in corpus (4)

• Anti-pre-Lie algebras, Novikov algebras and commutative 2-cocycles on Lie algebras
• Non-associative algebraic structures: classification and structure
• $\sigma$-matching and interchangeable structures on certain associative algebras
• Hochschild cohomology of the universal associative conformal envelope of the Virasoro Lie conformal algebra with coefficients in all finite modules