The Heisenberg-Virasoro Lie conformal superalgebra

Abstract

In this paper, we introduce a finite Lie conformal superalgebra called the Heisenberg-Virasoro Lie conformal superalgebra 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 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.