Dynamical Yang-Baxter equation and quantum vector bundles

Research output: Contribution to journalArticle


  • J. Donin
  • A. Mudrov


Publication details

JournalCommunications in Mathematical Physics
DatePublished - Mar 2005
Issue number3
Number of pages41
Pages (from-to)719-760
Original languageEnglish


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, 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 its 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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