The isomorphism problem for loops, that is, to know under which conditions the loop algebra isomorphism implies the loop isomorphism, is studied in the semisimple case for loops whose derived subloop is central. This is done by studying the structure of the semisimple loop algebra and by proving that it can be decomposed as a direct sum of an associative and commutative subalgebra with a nonassociative and non-commutative subalgebra.