Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A correspondence between a class of monoids and self-similar group
  actions II   The first author showed in a previous paper that there is a correspondence
between self-similar group actions and a class of left cancellative monoids
called left Rees monoids. These monoids can be constructed either directly from
the action using Zappa-Sz\'ep 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 signficant 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.

18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con