Orthogonal Completions of the Polycyclic Monoids

Abstract

We introduce the notion of an orthogonal completion of an inverse monoid with zero. We show that the orthogonal completion of the polycyclic monoid on n generators is isomorphic to the inverse monoid of right ideal isomorphisms between the finitely generated right ideals of the free monoid on n generators, and so we can make a direct connection with the Thompson groups V_n,1.

Keywords:

• Inverse semigroups
• Thompson groups

2000 AMS Subject Classification:

• 20F05
• 20M18