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.

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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

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article

Combinatorial twists in gl_n Yangians

Anastasia Doikou
Communications in Mathematics
semigroups and automata theory
article

Combinatorial twists in gl_n Yangians

Anastasia Doikou
article en

Abstract

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.

Communications in MathematicsVol. Volume 33 (2025), Issue 3...
Engineering and Physical Sciences Research Council
Openalex Percentile: Top 72%
semigroups and automata theory
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