Classification of compatible left-symmetric conformal algebras on solvable Lie conformal algebras of rank two
In this paper, we give a complete classification of compatible left-symmetric conformal algebra structures on solvable Lie conformal algebras which are free of rank two as $\mathbb{C}[\partial]$-modules up to isomorphism. We obtain ten mutually non-isomorphic normal-form types and determine the precise equivalence relations among the parameters within each family. Moreover, we also characterize the Novikov conformal algebras among the classified left-symmetric conformal algebras, thereby obtaining a complete classification of compatible Novikov conformal algebra structures in the same setting.
math.RA↗