Braided symmetries of $S{U}_{q,\varphi }(2)$ and Podleś Spheres

Abstract

We present an explicit form of braided symmetries of the quantum spheres, by introducing a braided quantum Hopf algebra $\cU_{q, ϕ}$ and demonstrating that they are braided Hopf modules over this braided Hopf algebra. To obtain this result, we systematically develop braided versions of structures like pairing between Hopf algebras, left module algebra as well as their compatibility with the $\ast$-structure.

16 pages, revised version

References in corpus (2)

• The Dirac operator on SU_q(2)
• Introduction to Braided Geometry and $q$-Minkowski Space