Braided Symmetries of SUq,ϕ(2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$SU_{q,\phi }(2)$$\end{document} and Podl

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