When unit groups of continuous inverse algebras are regular Lie groups

TL;DR

This paper investigates conditions under which the unit group of a continuous inverse algebra forms a regular Lie group, focusing on properties like Mackey-completeness and local m-convexity to ensure regularity.

Contribution

It provides new criteria guaranteeing the regularity of the unit group as a Lie group in the context of infinite-dimensional Lie theory.

Findings

G(A) is regular if A is Mackey-complete and locally m-convex

Established criteria for regularity of unit groups in continuous inverse algebras

Enhanced understanding of infinite-dimensional Lie group structures

Abstract

It is a basic fact in infinite-dimensional Lie theory that the unit group G(A) of a continuous inverse algebra A is a Lie group. We describe criteria ensuring that the Lie group G(A) is regular in Milnor's sense. Notably, G(A) is regular if A is Mackey-complete and locally m-convex.