扭Heisenberg-Virasoro 代数是Arbarello 等人首次研究的， 这里作者建立了某些由曲线组成的moduli 空间的二上同调跟阶数不超过1 的微分算子所生成的李代数的二上同调之间的一个联系。众所周知，它是一类无限维李代数，并且与full-toroidal 李代数和N = 2 的Neveu-Schwarz 超代数有关。因此，扭Heisenberg-Virasoro 代数的表示理论引起了很多数学家和物理学家的广泛关注。 本项目主要研究几类与扭Heisenberg-Virasoro 多项式模相关的非权模。

The twisted Heisenberg-Virasoro algebra was initially studied by Arbarello et al.，where a connection is established between the second cohomology of certain moduli spaces of curves and the second cohomology of the Lie algebra of differential operators of order at most of 1。 It is well-known that the twisted Heisenberg-Virasoro algebra is an infinite-dimensional Lie algebra, which has some relations with the full-toroidal Lie algebras and the N = 2 Neveu-Schwarz superalgebra。Therefore， the representation theory of the twisted Heisenberg-Virasoro algebra has attracted a lot of attention from mathematicians and physicists。 This project is to study the problem of some classes of non-weight modules over the twisted Heisenberg-Virasoro algebra, which are associated with a class of polynomial modules。