{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T10:38:03Z","timestamp":1772447883378,"version":"3.50.1"},"reference-count":23,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2015,6]]},"abstract":"<jats:p>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\u2013Sz\u00e9p 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.<\/jats:p>","DOI":"10.1142\/s0218196715500137","type":"journal-article","created":{"date-parts":[[2015,4,6]],"date-time":"2015-04-06T07:55:08Z","timestamp":1428306908000},"page":"633-668","source":"Crossref","is-referenced-by-count":10,"title":["A correspondence between a class of monoids and self-similar group actions II"],"prefix":"10.1142","volume":"25","author":[{"given":"Mark V.","family":"Lawson","sequence":"first","affiliation":[{"name":"Department of Mathematics, Heriot-Watt University, Riccarton, UK"},{"name":"Maxwell Institute for Mathematical Sciences, Edinburgh EH14 4AS, UK"}]},{"given":"Alistair R.","family":"Wallis","sequence":"additional","affiliation":[{"name":"School of Mathematical and Computer Sciences, Heriot-Watt University, No. 1 Jalan Venna P5\/2, Precinct 5, 62200 Putrajaya, Malaysia"}]}],"member":"219","published-online":{"date-parts":[[2015,5,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-4049(84)90055-0"},{"key":"rf2","volume-title":"El\u00e9ments de Math\u00e9matique, Alg\u00e8bre","author":"Bourbaki N.","year":"1970"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1081\/AGB-200047404"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/s00233-013-9490-y"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/007.1"},{"key":"rf6","volume-title":"Free Rings and their Relations","author":"Cohn P. 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