### A Pseudo-Analyzer Approach to Formal Group Laws not of Operad Type

**
Ralf Holtkamp
**

Formal group schemes, associated to affine group schemes or Lie groups
by completion, can be described by
classical formal group laws. More generally, cogroup objects
in categories of complete algebras (e.g. associative)
are described by group laws for operads or analyzers.
M.Lazard has introduced analyzers
to study formal group laws and group law chunks
(truncated formal power series).
A main example of a type of generalized formal group laws not
given by an operad or analyzer are group laws
corresponding to noncommutative complete Hopf algebras.
To cover this case and other types of group laws,
pseudo-analyzers are introduced. We point out differences
to the (quadratic) operad case, e.g. there is no
classification of group laws by
Koszul duality.
On the other hand we show how pseudo-analyzer cohomology
can be used to describe extension of group law chunks.