A class of non-graded left-symmetric algebraic structures on the Witt algebra

摘要

We classify the compatible left-symmetric algebraic structures on the Witt algebra satisfying certain non-graded conditions. It is unexpected that they are Novikov algebras. Furthermore, as applications, we study the induced non-graded modules of the Witt algebra and the induced Lie algebras by Novikov-Poisson algebras' approach and Balinskii-Novikov's construction.