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.