Direct limits of infinite-dimensional Carnot groups

TL;DR

This paper constructs direct limits of infinite-dimensional Carnot groups within complete metric scalable groups and proves a Rademacher-type theorem for these limits, advancing understanding of their geometric and analytic properties.

Contribution

It introduces a method to construct direct limits of infinite-dimensional Carnot groups and establishes conditions under which these limits retain Carnot group structure.

Findings

Successful construction of direct limits in the category of complete metric scalable groups.

Identification of sufficient conditions for the limits to be infinite-dimensional Carnot groups.

Proved a Rademacher-type theorem applicable to these limits.

Abstract

We give a construction of direct limits in the category of complete metric scalable groups and provide sufficient conditions for the limit to be an infinite-dimensional Carnot group. We also prove a Rademacher-type theorem for such limits.