A New Class Of Modules For Higher Rank Virasoro-Like Algebras

Virasoro-like algebra is a highly important infinite-dimensional Lie algebra that finds significant applications in numerous branches of mathematics and physics.The modulus and structure of the Virasoro-like algebra have been studied extensively,and considerable results have been obtained.The Lie algebra obtained by the higher rank generalization of Virasoro-like algebra is called higher rank Virasoro-like algebra.This paper focuses on the study of modules of higher rank Virasoro-like algebra.We construct a class new of modules Fdα for higher rank Virasoro-like algebra L and some of their submodules.We give sufficient and necessary conditions for Fdα and Fdβ to be isomorphism.It is proved that the submodules of Fdα are graded modules.And finally,we give a sufficient condition for the submodule W of Fdα to be equal to Fdα and find six composition series of F₂^?.