Combinatorial twists in gl_n Yangians
We introduce the special set-theoretic Yang-Baxter algebra and show that it is a Hopf algebra subject to certain conditions. The associated universal R-matrix is also obtained via an admissible Drinfel'd twist. The structure of braces emerges naturally in this context by requiring the special set-theoretic Yang-Baxter algebra to be a Hopf algebra and a quasi-triangular bialgebra after twisting. The fundamental representation of the universal R-matrix yields the familiar set-theoretic (combinatorial) solutions of the Yang-Baxter equation. We then apply the same Drinfel'd twist to the gl_n Yangian after introducing the augmented Yangian. We show that the augmented Yangian is also a Hopf algebra and we also obtain its twisted version.
Authors
- Anastasia Doikou (ORCID: https://orcid.org/0000-0001-6869-9389)
Publication Details
- Journal
- Communications in Mathematics
- Published
- 2025-09-26
- DOI
- https://doi.org/10.46298/cm.15770
- Primary Topic
- semigroups and automata theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Engineering and Physical Sciences Research Council