Dynamical Yang-Baxter equation and quantum vector bundles

Details Dynamical Yang-Baxter equation and quantum vector bundles Dynamical Yang-Baxter equation and quantum vector bundles

2003-06-02

arxiv.org/abs/math/0306028v3

Mathematics

Quantum Algebra

55 pages, AMS Latex, some corrections and additions

Scientific paper

We develop a categorical approach to the dynamical Yang-Baxter equation (DYBE) for arbitrary Hopf algebras. In particular, we introduce the notion of a dynamical extension of a monoidal category, which provides a natural environment for quantum dynamical R-matrices, dynamical twists, {\em etc}. In this context, we define dynamical associative algebras and show that such algebras give quantizations of vector bundles on coadjoint orbits. We build a dynamical twist for any pair of a reductive Lie algebra and their Levi subalgebra. Using this twist, we obtain an equivariant star product quantization of vector bundles on semisimple coadjoint orbits of reductive Lie groups.

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