  Associative conformal algebras of conformal endomorphisms are of essential
importance for the study of finite representations of conformal Lie algebras
(Lie vertex algebras). We describe all semisimple algebras of conformal
endomorphisms which have the trivial second Hochschild cohomology group with
coefficients in every conformal bimodule. As a consequence, we state a complete
solution of the radical splitting problem in the class of associative conformal
algebras with a finite faithful representation.
