Abstract
The first author showed in a previous paper that there is a correspondence between selfsimilar group actions and a class of left cancellative monoids called left Rees monoids. These monoids can be constructed either directly from the action using ZappaSzép products, a construction that ultimately goes back to Perrot, or as left cancellative tensor monoids from the covering bimodule, utilizing a construction due to Nekrashevych. In this paper, we generalize the tensor monoid construction to arbitrary bimodules. We call the monoids that arise in this way Levi monoids and show that they are precisely the equidivisible monoids equipped with length functions. Left Rees monoids are then just the left cancellative Levi monoids. We single out the class of irreducible Levi monoids and prove that they are determined by an isomorphism between two divisors of its group of units. The irreducible Rees monoids are thereby shown to be determined by a partial automorphism of their group of units; this result turns out to be significant since it connects irreducible Rees monoids directly with HNN extensions. In fact, the universal group of an irreducible Rees monoid is an HNN extension of the group of units by a single stable letter and every such HNN extension arises in this way.
Original language  English 

Pages (fromto)  633668 
Number of pages  36 
Journal  International Journal of Algebra and Computation 
Volume  25 
Issue number  4 
Early online date  28 Apr 2015 
DOIs  
Publication status  Published  Jun 2015 
Keywords
 HNN extensions
 left cancellative monoids
 Selfsimilar group actions
ASJC Scopus subject areas
 Mathematics(all)
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Mark Lawson
 School of Mathematical & Computer Sciences  Professor
 School of Mathematical & Computer Sciences, Mathematics  Professor
Person: Academic (Research & Teaching)