2024/06/14 by Davide Ferri, Andrea Sciandra, Ferri, Davide +1 · 2 citations
Engineering · Mathematics · #18M15 #Category Theory (math.CT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Primary 16T05 #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Secondary 16T25 #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.2406.10009
openalex publication_date 2024/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is proven that a matched pair of actions on a Hopf algebra H is equivalent to the datum of a Yetter-Drinfeld brace, which is a novel structure generalising Hopf braces. This improves a theorem by Angiono, Galindo and Vendramin, originally stated for cocommutative Hopf braces. These Yetter-Drinfeld braces produce Hopf algebras in the category of Yetter-Drinfeld modules over H, through an operation that generalises Majid's transmutation. A characterisation of Yetter-Drinfeld braces via 1-cocycles, in analogy to the one for Hopf braces, is given. Every coquasitriangular Hopf algebra H will be seen to yield a Yetter-Drinfeld brace, where the additional structure on H is given by the transmutation. We compute explicit examples of Yetter-Drinfeld braces on the Sweedler's Hopf algebra, on the algebras E(n), on SLq(2), and an example in the class of Suzuki algebras.