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.