Abstract
We consider involutive, non-degenerate, finite set-theoretic solutions of the Yang-Baxter equation (YBE). Such solutions can be always obtained using certain algebraic structures that generalize nilpotent rings called braces. Our main aimhere is to express such solutions in terms of admissible Drinfeld twists substantially extending recent preliminary results. We first identify the generic form of the twists associated to set-theoretic solutions and we show that these twists are admissible, i.e. they satisfy a certain co-cycle condition. These findings are also valid for Baxterized solutions of the YBE constructed from the set-theoretical ones.
Original language | English |
---|---|
Article number | 415201 |
Journal | Journal of Physics A: Mathematical and Theoretical |
Volume | 54 |
Issue number | 41 |
Early online date | 26 Aug 2021 |
DOIs | |
Publication status | Published - 15 Oct 2021 |
Keywords
- Braces
- Drinfeld twists
- Quantum groups
- Yang-Baxter equation
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- General Physics and Astronomy