A remarkable family of left ordered groups: central extensions of Hecke groups

TL;DR

This paper introduces an infinite family of left-ordered groups, including well-known groups like the Klein bottle group and B_3, with finitely generated positive cones, expanding understanding of orderability in group theory.

Contribution

It constructs a new family of left-ordered groups as central extensions of Hecke groups, with finitely generated positive cones, highlighting novel examples in group orderability.

Findings

Includes the Klein bottle group and B_3 in the family

Shows positive cones are finitely generated as semigroups

Provides new examples of left-ordered groups

Abstract

We provide an infinite family of left-ordered groups, all of which have a positive cone that is finitely generated as a semigroup. This family includes the Klein bottle group and the braid group B_3.