Locally Compact Contractive Local Groups

TL;DR

This paper investigates the structure of locally compact contractive local groups, showing that locally connected cases resemble Lie groups and providing a broader structure theorem for the general case.

Contribution

It establishes that locally connected locally compact contractive local groups are locally isomorphic to Lie groups, extending known theorems to local groups.

Findings

Locally connected contractive local groups are locally isomorphic to Lie groups.

A structure theorem is proved for all locally compact contractive local groups.

Results are local analogues of theorems for globally contractive groups.

Abstract

We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also prove a related structure theorem for locally compact contractive local groups which are not necessarily locally connected. These results are local analogues of theorems for locally compact contractive groups.