Dynamical Yang-Baxter equation and quantum vector bundles

We develop a categorical approach to the dynamical Yang-Baxter equation (DYBE) for arbitrary Hopf algebras. In particular, we introduce a notion of dynamical extension of a monoidal category, which provides a natural environment for quantum dynamical R-matrices. In this context, we define dynamical associative algebras and show that such algebras give a quantization of vector bundles on coadjoint orbits. Using the relation between dynamical associative algebras and quantum vector bundles we build a dynamical twist for the pair of a simple Lie algebra and its Levi subalgebra.