2025/02/28 by Rodríguez, Ramón González, Pérez, Brais Ramos
#16S35 #16S40 #16T05 #18M05 #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2502.20919
The present article represents a step forward in the study of the following problem: If \mathbbA=(A1,A2) and ℍ=(H1,H2) are Hopf braces in a symmetric monoidal category C such that (A1,H1) and (A2,H2) are matched pairs of Hopf algebras, then we want to know under what conditions the pair (A1\bowtie H1,A2\bowtie H2) constitutes a new Hopf brace. We find such conditions for the pairs (A1⊗ H1,A2\bowtie H2) and (A1\bowtie H1,A2\sharp H2) to be Hopf braces, which are particular situations of the general problem described above, and we apply these results to study when the Drinfeld's Double gives rise to a Hopf brace.