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In this paper, a class of super Heisenberg-Virasoro algebras is introduced on the base of conformal modules of Lie conformal superalgebras. Then we construct a class of simple super Heisenberg-Virasoro modules, which is induced from simple modules of the finite-dimensional solvable Lie superalgebras. These modules are isomorphic to simple restricted super Heisenberg-Virasoro modules, and include the highest weight modules, Whittaker modules and high order Whittaker modules.
Let $mathfrak g(G,lambda)$ denote the deformed generalized Heisenberg-Virasoro algebra related to a complex parameter $lambda eq-1$ and an additive subgroup $G$ of $mathbb C$. For a total order on $G$ that is compatible with addition, a Verma module
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 $mathrm{Ind}(M)$ that we obtain a class of n
In this paper, we classify all indecomposable Harish-Chandra modules of the intermediate series over the twisted Heisenberg-Virasoro algebra. Meanwhile, some bosonic modules are also studied.
A double extension ($mathscr{D}$ extension) of a Lie (super)algebra $mathfrak a$ with a non-degenerate invariant symmetric bilinear form $mathscr{B}$, briefly: a NIS-(super)algebra, is an enlargement of $mathfrak a$ by means of a central extension an
In this paper, we classify the compatible left-symmetric superalgebra structures on the super-Virasoro algebras satisfying certain natural conditions.