  In this paper, we develop a cohomology theory of a left-symmetric conformal
algebra and study its some applications. We define the cohomology of a
left-symmetric conformal algebra, and then give an isomorphism between the
cohomology spaces of the left-symmetric conformal algebra and its sub-adjacent
Lie conformal algebra. As applications of the cohomology theory, we study
linear deformations, formal $1$-parameter deformations, $T^*$-extensions of a
left-symmetric conformal algebra respectively and obtain some properties.

Rings and Algebras