A class of graded conformal algebras which is induced by Heisenberg-Virasoro conformal algebra

Abstract

In this paper, we obtain a class of Z-graded conformal algebras which is induced by Heisenberg-Virasoro conformal algebra. More precisely, we classify Z-graded conformal algebrasFurther, we prove that all finite nontrivial irreducible modules of these algebras under some special conditions are free of rank one as a C[∂]-module. The conformal derivations of this class of graded Lie conformal algebras are also determined.