This article investigates conditions to form new Hopf braces in algebraic structures, highlighting implications for quantum equations.
The present article represents a step forward in the study of the following problem: If A=(A₁,A₂) and H=(H₁,H₂) are Hopf braces in a symmetric monoidal category such that (A₁,H₁) and (A₂,H₂) are matched pairs of Hopf algebras, then we want to know under what conditions the pair (A₁ H₁,A₂ H₂) constitutes a new Hopf brace. We find such conditions for the pairs (A₁⊗ H₁,A₂ H₂) and (A₁ H₁,A₂ H₂) to be Hopf braces, which are particular situations of the general problem described above, analyzing when these are cocommutative, leading to solutions to the Quantum Yang-Baxter equation. These results are applied to study when the Drinfeld’s Double gives rise to a Hopf brace.
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Rodríguez et al. (2026) studied this question.
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