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Communications in Mathematical Physics

, Volume 254, Issue 3, pp 719–760 | Cite as

Dynamical Yang-Baxter Equation and Quantum Vector Bundles

  • J. Donin
  • A. Mudrov
Article
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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.

Keywords

Vector Bundle Hopf Algebra Associative Algebra Quantum Vector Categorical Approach 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • J. Donin
    • 1
  • A. Mudrov
    • 1
  1. 1.Department of MathematicsBar Ilan UniversityRamat GanIsrael

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