What does this research mean for the field?

Quantum spheres are U_{q, \phi} braided Hopf module algebras and represent the unique quadratic algebras generated by the fundamental representation of U_{q, \phi} that act as braided U_{q, \phi}-modules. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To formulate the braided symmetries associated with quantum spheres using the braided quantum Hopf algebra.

June 7, 2026Open Access

Braided Symmetries of SUₐ, (2) and Podleś Spheres

RBRafał BistrońJagiellonian University ASAndrzej SitarzJagiellonian University

Puntos clave

To formulate the braided symmetries associated with quantum spheres using the braided quantum Hopf algebra.
Introduced the braided quantum Hopf algebra Uq,φ.
Demonstrated quantum spheres as Uq,φ braided Hopf module algebras.
Analyzed quadratic algebras generated by the fundamental representation of Uq,φ.
Showed that quantum spheres are Uq,φ braided Hopf module algebras.
Confirmed that they are the only quadratic algebras from the fundamental representation of Uq,φ that function as braided Uq,φ-modules.

Resumen

We present an explicit formulation of the braided symmetries of quantum spheres by introducing a braided quantum Hopf algebra {U}ₐ, and demonstrating that the quantum spheres are {U}ₐ, braided Hopf module algebras. Furthermore, we demonstrate that they are the only quadratic algebras generated by the fundamental representation of {U}ₐ, which are braided {U}ₐ, -modules.

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