A recent explosion of algebraic structures derived in quantum field theory [14, 15] and in the theory of vertex operator algebras [13] has led to the renaissance of operads and algebras with several operations. The physicists’ vision of the Universe revealed evidence of a number of new mathematical structures now being intensively studied by mathematicians,[6, 7, 8, 9, 11, 13]. Comparing the two results:(1)(Gerstenhaber,[4]) The Hochschild cohomology HH•(A):= H•(A, A) of an associative algebra A has a natural structure of a G algebra, short for a Gerstenhaber algebra.(2)(F. Cohen,[2]) An algebra over the homology little squares operad is nothing but a G algebra. and, perhaps, the new insights on homotopy algebras [8, 12], P. Deligne posed the following conjecture in his letter [3].