This research presents braided quantum Hopf algebras in relation to quantum spheres, suggesting unique properties for these structures.
We present an explicit formulation of the braided symmetries of quantum spheres by introducing a braided quantum Hopf algebra Uq, φ and demonstrating that the quantum spheres are Uq, φ braided Hopf module algebras. Furthermore, we demonstrate that they are the only quadratic algebras generated by the fundamental representation of Uq, φ which are braided Uq, φ -modules.
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Bistroń et al. (2026) studied this question.
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