LAUSR

The ℂ[∂]$\mathbb {C}[\partial ]$-split extending structures problem for Lie conformal algebras is studied. In this paper, we introduce the definition of unified product of a given Lie conformal algebra R and a given ℂ[∂]$\mathbb {C}[\partial ]$-module Q. This product includes some other interesting products of Lie conformal algebras such as twisted product, crossed product, and bicrossed product. Using this product, a cohomological type object is constructed to provide a theoretical answer to the ℂ[∂]$\mathbb {C}[\partial ]$-split extending structures problem. Moreover, using this general theory, we investigate crossed product and bicrossed product in detail, which give the answers for the ℂ[∂]$\mathbb {C}[\partial ]$-split extension problem and the ℂ[∂]$\mathbb {C}[\partial ]$-split factorization problem respectively.