Integrating Hasse-Schmidt derivations

TL;DR

This paper investigates the integration of Hasse-Schmidt derivations satisfying formal group law conditions, extending previous theorems on nilpotent and idempotent derivations within algebraic structures.

Contribution

It generalizes existing theorems on integrating derivations to broader classes satisfying formal group law conditions, specifically for additive and multiplicative cases.

Findings

Extended Matsumura's theorem to broader derivations

Generalized Tyc's theorem for idempotent derivations

Analyzed derivations under formal group law conditions

Abstract

We study integrating (that is expanding to a Hasse-Schmidt derivation) derivations, and more generally truncated Hasse-Schmidt derivations, satisfying iterativity conditions given by formal group laws. Our results concern the cases of the additive and the multiplicative group laws. We generalize a theorem of Matsumura about integrating nilpotent derivations (such a generalization is implicit in work of Ziegler) and we also generalize a theorem of Tyc about integrating idempotent derivations.