Algebraic constructions for left-symmetric conformal algebras

Abstract

Let R be a left-symmetric conformal algebra and Q be a C [ ∂ ] -module. We introduce the notion of a unified product for left-symmetric conformal algebras and apply it to construct an object H R 2 ( Q , R ) to describe and classify all left-symmetric conformal algebra structures on the direct sum E = R ⊕ Q as a C [ ∂ ] -module such that R is a subalgebra of E up to isomorphism whose restriction on R is the identity map. Moreover, we study H R 2 ( Q , R ) in detail when Q, R are free as C [ ∂ ] -modules and rank Q = 1 . Some special products such as crossed product and bicrossed product are also investigated.