2021/05/07 by Aryan Ghobadi, Ghobadi, Aryan
Mathematics · Physics and Astronomy · #16T25 #16T99 #17B37 #18M15 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2105.03286
openalex publication_date 2021/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the notion of Drinfeld twists for both set-theoretical YBE solutions and skew braces. We give examples of such twists and show that all twists between skew braces come from families of isomorphisms between their additive groups. We then describe the relation between these definitions and co-twists on FRT-type Hopf algebras in the category SupLat, and prove that any co-twist on a co-quasitriangular Hopf algebra in SupLat induces a Drinfeld twist on its remnant skew brace. We go on to classify co-twists on bicrossproduct Hopf algebras coming from groups with unique factorisation, and the twists which they induce on skew braces.