Another class of simple graded Lie conformal algebras that cannot be embedded into general Lie conformal algebras

In a previous paper by the authors, we obtain the first example of a finitely freely generated simple Z-graded Lie conformal algebra of linear growth that cannot be embedded into any general Lie conformal algebra. In this paper, we obtain, as a byproduct, another class of such Lie conformal algebras by classifying Z-graded simple Lie conformal algebras G = circle plus(infinity)(i=-1) G(i) satisfying the following, (1) G(0) congruent to Vir, the Virasoro conformal algebra; (2) Each G(i) for i >= -1 is a Vir-module of rank one. (c) 2021 Published by Elsevier Inc.These algebras include some Lie conformal algebras of Block type.