Lie pairs and formal Lie groups

TL;DR

This paper develops the theory of formal Lie groups, showing their equivalence to Lie pairs, thus extending classical formal Lie theory within the framework of formal manifolds.

Contribution

It introduces formal Lie groups as group objects in formal manifolds and establishes their categorical equivalence to Lie pairs, broadening the scope of formal Lie theory.

Findings

Formal Lie groups are shown to be equivalent to Lie pairs.

The paper extends classical formal Lie theory to the setting of formal manifolds.

Foundational properties of formal Lie groups are established.

Abstract

In a previous paper, we introduce and study formal manifolds, which generalize smooth manifolds. In this paper, we establish the basic theory of formal Lie groups, which are group objects in the category of formal manifolds. In particular, extending the classical formal Lie theory theorem, we prove that the category of formal Lie groups is equivalent to the category of Lie pairs.