Set-theoretic Yang–Baxter equation, braces and Drinfeld twists. (15th September 2021)

• Record Type: Journal Article
• Authors: Doikou, Anastasia
• Is Part Of: Journal of physics. Volume 54:Number 41(2021)
• Publication Date: 2021-09-15
• Subjects: Yang–Baxter equation -- braces -- quantum groups -- Drinfeld twists; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ac219e
• Languages: English
• ISSNs: 1751-8113

Abstract

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 aim here 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.