Extending structures of lie conformal superalgebras

Abstract

In this article, we generalize the -split extending structures problem of Lie conformal algebras to the super case. First, we introduce a unified product of a given Lie conformal superalgebra and a given -graded -module Q. This product includes some other products such as the twisted product, crossed product, and bicrossed product. Second, using these products, we describe and classify all Lie conformal superalgebra structures on when and Q satisfy some conditions.