  We show for bicommutative graded connected Hopf algebras that a certain
distributive (Laplace) subgroup of the convolution monoid of 2-cochains
parameterizes certain well behaved Hopf algebra deformations. Using the Laplace
group, or its Frobenius subgroup, we define higher derived hash products, and
develop a general theory to study their main properties. Applying our results
to the (universal) bicommutative graded connected Hopf algebra of symmetric
functions, we show that classical tensor product and character decompositions,
such as those for the general linear group, mixed co- and contravariant or
rational characters, orthogonal and symplectic group characters, Thibon and
reduced symmetric group characters, are special cases of higher derived hash
products. In the Appendix we discuss a relation to formal group laws.
