The Heisenberg-Virasoro Lie conformal superalgebra

Abstract

In this paper, we introduce a finite Lie conformal superalgebra called the Heisenberg-Virasoro Lie conformal superalgebra $\mathfrak{s}$ by using a class of Heisenberg-Virasoro Lie conformal modules. The super Heisenberg-Virasoro algebra of Ramond type $\S$ is defined by the formal distribution Lie superalgebra of $\mathfrak{s}$. Then we construct a class of simple $\S$-modules, which are induced from simple modules of some finite dimensional solvable Lie superalgebras. These modules are isomorphic to simple restricted $\S$-modules, and include the highest weight modules, Whittaker modules and high order Whittaker modules. As a byproduct, we present a subalgebra of $\S$, which is isomorphic to the super Heisenberg-Virasoro algebra of Neveu-Schwarz type.

References in corpus (8)

• Formal distribution algebras and conformal algebras
• Whittaker Modules for the twisted Heisenberg-Virasoro Algebra
• Characterization of simple highest weight modules
• A family of non-weight modules over the super-Virasoro algebras
• Simple weak modules for the fixed point subalgebra of the Heisenberg vertex operator algebra of rank $1$ by an automorphism of order $2$ and Whittaker vectors
• Classification of simple Harish-Chandra modules over the N=1 Ramond algebra
• On irreducibility of modules of Whittaker type for cyclic orbifold vertex algebra
• A family of new simple modules over the Schrödinger-Virasoro algebra

Cited by in corpus (1)

• Whittaker modules for classical Lie superalgebras