Abstract
The \(\mathbb {C}[\partial ]\)-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 \(\mathbb {C}[\partial ]\)-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 \(\mathbb {C}[\partial ]\)-split extending structures problem. Moreover, using this general theory, we investigate crossed product and bicrossed product in detail, which give the answers for the \(\mathbb {C}[\partial ]\)-split extension problem and the \(\mathbb {C}[\partial ]\)-split factorization problem respectively.
Published Version
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