Dehornoy-like left orderings and isolated left orderings

TL;DR

This paper introduces a new class of group orderings called Dehornoy-like orderings, generalizing braid group orderings, and explores their properties, including the creation of isolated orderings and new examples under a specific property.

Contribution

It defines Dehornoy-like orderings, establishes their properties under Property F, and constructs new examples of such orderings and isolated orderings.

Findings

Dehornoy-like orderings share properties with the original Dehornoy ordering.

Under Property F, these orderings produce isolated left orderings.

New examples of Dehornoy-like and isolated orderings are constructed.

Abstract

We introduce a Dehornoy-like ordering of groups, which is a generalization of the Dehornoy ordering of the braid groups. Under a weak assumption which we call Property F, we show that Dehornoy-like orderings have properties similar to the Dehornoy ordering, and produce isolated left orderings. We also construct new examples of Dehornoy-like ordering and isolated orderings and study their more precise properties.