A new class of Z-graded Lie conformal algebras of infinite rank

Abstract: In this paper, a new class of $\Z$-graded Lie conformal algebras $\CW(a,c)$ of infinite rank is constructed. The conformal derivations and one-dimensional central extensions of $\CW(a,c)$ are completely determined. And all conformal modules of rank one over $\CW(a,c) (a\neq0)$ are proved to be trivial and all such nontrivial (irreducible) modules over $\CW(0,c)$ are classified.