Description of infinite dimensional abelian regular Lie groups

TL;DR

This paper demonstrates that all abelian regular Lie groups can be represented as quotients of their Lie algebras through the exponential map, extending understanding of their structure.

Contribution

It establishes a universal property for abelian regular Lie groups, showing they are quotients of their Lie algebras via the exponential map, which was not previously known.

Findings

Every abelian regular Lie group is a quotient of its Lie algebra.

The exponential map provides a surjective homomorphism in this context.

This result characterizes the structure of abelian regular Lie groups.

Abstract

It is shown that every abelian regular Lie group is a quotient of its Lie algebra via the exponential mapping.