Quasi-bialgebras from set-theoretic type solutions of the Yang-Baxter equation
type: Item
instance of: scholarly article
title: Quasi-bialgebras from set-theoretic type solutions of the Yang-Baxter equation
author: Anastasia Doikou
author: Alexandros Ghionis
author: Bart Vlaar
published in: Letters in Mathematical Physics
publication date: 2022-09-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/2203.03400
review text: There is an interest in studying classes of quantum algebras arising from set-theoretic solutions of the Yang-Baxter equation. The motivations for deepening this investigation lie in the paper [\textit{A. Doikou} and \textit{A. Smoktunowicz}, Lett. Math. Phys. 111, No. 4, Paper No. 105, 40 p. (2021; Zbl 1486.16039)]. In the paper under review, the authors investigate algebras coming from involutive and non-degenerate solutions and their \(q\)-analogues. It is shown that they are quasi-triangular quasi-bialgebras. To get this result, they provide some universal results on quasi-bialgebras and admissible Drinfeld twists. In fact, the property of being quasi-triangular (quasi-)bialgebra is preserved by twisting (see [\textit{V. G. Drinfel'd}, Sov. Math., Dokl. 32, 256--258 (1985; Zbl 0588.17015); translation from Dokl. Akad. Nauk SSSR 283, 1060--1064 (1985)]). Moreover, they make use of some first results on the admissible Drinfeld twist for involutive set-theoretic solution already derived in [\textit{A. Doikou}, J. Phys. A, Math. Theor. 54, No. 41, Article ID 415201, 21 p. (2021; Zbl 07654521)].
reviewed by: Marzia Mazzotta
Mathematics Subject Classification ID: 16T20
Mathematics Subject Classification ID: 16T25
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 20G42
zbMATH DE Number: 7583939
zbMATH Keywords: quasi-bialgebras
zbMATH Keywords: set-theoretic Yang-Baxter equation
zbMATH Keywords: Drinfeld twists
MaRDI profile type: Publication
OpenAlex ID: W4290722538
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DOI: 10.1007/S11005-022-01572-9
description: scientific article; zbMATH DE number 7583939