There exist natural generalizations of the concept
of formal group laws for noncommutative power series.
This is a note on formal quantum group laws
and quantum group law chunks.
Formal quantum group laws correspond
to noncommutative (topological) Hopf algebra structures on
free associative power series algebras
K<< x_1,...,x_m >>, K a field.
Some formal quantum group laws occur as completions
of noncommutative Hopf algebras (quantum groups).
By truncating formal power series,
one gets quantum group law chunks.

If the characteristic of K is 0, the category
of (classical) formal group laws of given dimension m is
equivalent to the category of m-dimensional Lie algebras.
Given a formal group law or quantum group law (chunk),
the corresponding Lie structure constants are determined by the
coefficients of its chunk of degree 2.
Among other results, a classification of all quantum group
law chunks of degree 3 is given. There are many more
classes of strictly isomorphic chunks of degree 3
than in the classical case.