Related papers: Two classes of non-weight modules over the twisted…
In this paper, we realize polynomial $\H$-modules $\Omega(\lambda,\alpha,\beta)$ from irreducible twisted Heisenberg-Virasoro modules $\A_{\alpha,\beta}$. It follows from $\H$-modules $\Omega(\lambda,\alpha,\beta)$ and $\mathrm{Ind}(M)$…
In this paper, we present a class of non-weight Virasoro modules $\mathcal{M}\big(V,\Omega(\lambda_0,\alpha_0)\big)\otimes\bigotimes_{i=1}^m\Omega(\lambda_i,\alpha_i)$ where $\Omega(\lambda_i,\alpha_i)$ and…
In this paper, we construct a class of non-weight modules over the affine-Virasoro algebra of type $A_1$ by taking tensor products of a finite number of irreducible modules $M(\lambda, \alpha, \beta, \gamma)$ with irreducible highest weight…
In this paper, we obtain a class of Virasoro modules by taking tensor products of the irreducible Virasoro modules $\Omega(\lambda,\alpha,h)$ and $\Omega(\mu, b)$ with irreducible highest weight modules $V(\theta,h)$ or with irreducible…
In this paper, we study irreducible non-weight modules over the mirror Heisenberg-Virasoro algebra $\mathcal{D}$, including Whittaker modules, $\mathcal{U}(\mathbb{C} d_0)$-free modules, and their tensor products. More precisely, we give…
In this paper, we obtain a class of Virasoro modules by taking tensor products of the irreducible Virasoro modules $\Omega(\lambda,\alpha,h)$ defined in \cite{CG}, with irreducible highest weight modules $V(\theta,h)$ or with irreducible…
For a simple module $M$ over the positive part of the Virasoro algebra (actually for any simple module over some finite dimensional solvable Lie algebras $\mathfrak{a}_r$) and any $\alpha\in\C$, a class of weight modules $\mathcal {N}(M,…
Let $\mathcal{B}_r$ be the $(r+1)$-dimensional quotient Lie algebra of the positive part of the Virasoro algebra $\mathcal{V}$. Irreducible $\mathcal{B}_r$-modules were used to construct irreducible Whittaker modules in [MZ2] and…
In this paper, all irreducible weight modules with finite dimensional weight spaces over the twisted Heisenberg-Virasoro algebra are determined. There are two different classes of them. One class is formed by simple modules of intermediate…
In this paper, we study irreducible weight modules with infinite dimensional weight spaces over the mirror-twisted Heisenberg-Virasoro algebra $\mathcal{D}$. More precisely, the necessary and sufficient conditions for the tensor products of…
In this paper, we obtain a class of irreducible Virasoro modules by taking tensor products of the irreducible Virasoro modules $\Omega(\lambda,b)$ defined in [LZ], with irreducible highest weight modules $V(\theta,h)$ or with irreducible…
For any triple $(\mu,\lambda,\alpha)$ of complex numbers and an $\mathfrak a$-module ${V}$, a class of non-weight modules $\mathcal{M}\big(V,\mu,\Omega(\lambda,\alpha)\big)$ over the Virasoro algebra $\mathcal L$ is constructed in this…
We use Block's results to classify irreducible modules over the differential operator algebra $\mathbb{C}[t,t^{-1}, \frac d{dt}]$. From this classification and using "the twisting technique" we construct a lot of new irreducible modules…
In this paper, we construct a class of non-weight modules over the affine-Virasoro algebra of type $A_1$ by taking tensor products of irreducibles defined in [Q. Chen, J. Han, Non-weight modules over the affine-Virasoro algebra of type…
In this paper, we study a class of non-weight modules over the generalized Heisenberg-Virasoro algebra of rank two $\widetilde{L}(p_1, p_2)$. We construct a family of irreducible $\widetilde{L}(p_1, p_2)$-modules, determine the isomorphism…
We first define a class of non-weight modules over the N=1 Heisenberg-Virasoro superalgebra $\mathfrak{g}$, which are reducible modules. Then we give all submodules of such modules, and present the corresponding irreducible quotient modules…
In this paper, we study the tensor products of irreducible highest weight modules with irreducible loop modules over the affine-Virasoro algebra with aid of the ``shifting technique" established for the Virasoro algebra in [H. Chen, X. Guo,…
In this paper, we study a class of non-weight modules over two kinds of algebras related to the Virasoro algebra, i.e., the loop-Virasoro algebras $\mathfrak{L}$ and a class of Block type Lie algebras $\mathfrak{B(q)}$, where $q$ is a…
In this paper, we study non-weight modules over gap-$p$ Virasoro algebras, including Whittaker modules, $\mathcal{U}(\mathbb{C} L_0)$-free modules and their tensor products. We establish necessary and sufficient conditions for universal…
We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, which has an infinite dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module…