Extending structures for associative conformal algebras

In this paper, we give a study of the -split extending structures problem for associative conformal algebras. Using the unified product as a tool, which includes interesting products such as bicrossed product, cocycle semi-direct product and so on, a cohomological type object is constructed to characterize the -split extending structures for associative conformal algebras. Moreover, using this theory, the extending structures of an associative conformal algebra A which is free as a -module by the -module are described using flag datums of A. Furthermore, we give a classification of the extending structures of A by in detail up to equivalence when A is a free associative conformal algebra of rank1.