The center of a rational cohomology algebra for some loop spaces with respect to the Pontryagin product

We solve the problem of calculation of the center of the rational cohomology algebra H*(ΩX;?) of the loop space of simply connected four-dimensional manifolds with the Pontryagin product. The well-known results of Milnor and Moore represent H*(ΩX) as a universal enveloping Lie algebra π*(ΩX) endowed with the Whitehead-Samelson bracket. Neisendorfer obtained a representation of the algebra Π*(ΩX) ? ? in terms of generators and relations for the case when X is a simply connected four-dimensional manifold. In this paper, the center Z(H*(ΩX;?)) is calculated using this representation.