The Yang-Baxter equation and Thompson's group F

Research output: Contribution to journalArticlepeer-review


We define non-degenerate involutive partial solutions as a generalization of non-degenerate involutive set-theoretical solutions of the quantum Yang-Baxter 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's group F. This raises the question of whether there are further connections between partial solutions and Thompson's groups in general.

Original languageEnglish
JournalInternational Journal of Algebra and Computation
Issue number3
StateAccepted/In press - 2023

Bibliographical note

Publisher Copyright:
© 2023 World Scientific Publishing Company.


  • braces
  • Set-theoretic solutions of the Yang-Baxter equation
  • Thompson groups

ASJC Scopus subject areas

  • Mathematics (all)


Dive into the research topics of 'The Yang-Baxter equation and Thompson's group F'. Together they form a unique fingerprint.

Cite this