Abstract
In this paper,we consider Lie conformal algebras with derivations.A pair consisting of a Lie conformal algebra and a distinguished derivation is called a LieCDer pair.We introduce a cohomology theory for LieCDer pair with coefficients in a representation.Furthermore,we study abelian extensions of a LieCDer pair as an application of cohomology theory.Finally,we consider homotopy derivations on 2-term conformal Loo-algebras and 2-derivations on conformal Lie 2-algebras.The category of 2-term conformal Loo-algebras with homotopy derivations is equivalent to the category of conformal Lie 2-algebras with 2-derivations.
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