Dynamical Yang-Baxter equation and quantum vector bundles

J. Donin, A. Mudrov

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)719-760
Number of pages42
JournalCommunications in Mathematical Physics
Volume254
Issue number3
DOIs
StatePublished - Mar 2005

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