Graded Lie Conformal Algebras Induced by Rank-Two Lie Conformal Algebras

In this paper, we classify [Formula: see text]-graded Lie conformal algebras [Formula: see text] under the following assumptions: (C1) [Formula: see text] is a free [Formula: see text]-module of rank two; (C2) each [Formula: see text] with [Formula: see text] is a free [Formula: see text]-module of rank one; (C3) [Formula: see text] for every [Formula: see text]. The proof is divided according to whether [Formula: see text] is solvable.