{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,14]],"date-time":"2026-02-14T05:29:17Z","timestamp":1771046957190,"version":"3.50.1"},"reference-count":50,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2023,5]]},"abstract":"<jats:p> We define non-degenerate involutive partial solutions as a generalization of non-degenerate involutive set-theoretical solutions of the quantum Yang\u2013Baxter equation (QYBE). The induced operator is not a classical solution of the QYBE, but a braiding operator as in conformal field theory. We define the structure inverse monoid of a non-degenerate involutive partial solution and prove that if the partial solution is square-free, then it embeds into the restricted product of a commutative inverse monoid and an inverse symmetric monoid. Furthermore, we show that there is a connection between partial solutions and Thompson\u2019s group F. This raises the question of whether there are further connections between partial solutions and Thompson\u2019s groups in general. <\/jats:p>","DOI":"10.1142\/s0218196723500261","type":"journal-article","created":{"date-parts":[[2023,3,10]],"date-time":"2023-03-10T06:33:45Z","timestamp":1678430025000},"page":"547-584","source":"Crossref","is-referenced-by-count":6,"title":["The Yang\u2013Baxter equation and Thompson\u2019s group <i>F<\/i>"],"prefix":"10.1142","volume":"33","author":[{"given":"Fabienne","family":"Chouraqui","sequence":"first","affiliation":[{"name":"University of Haifa at Oranim, Kiryat Tivon, Israel"}]}],"member":"219","published-online":{"date-parts":[[2023,4,28]]},"reference":[{"key":"S0218196723500261BIB002","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1016\/j.jalgebra.2016.01.011","volume":"453","author":"Bachiller D.","year":"2016","journal-title":"J. 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