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Dynamical Yang-Baxter equation and quantum vector bundles

Donin, J. and Mudrov, A. (2005) Dynamical Yang-Baxter equation and quantum vector bundles. Commun. Math. Phys., 254 (3). pp. 719-760. ISSN 1432-0916

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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.

Item Type: Article
Academic Units: The University of York > Mathematics (York)
Depositing User: York RAE Import
Date Deposited: 12 Jun 2009 11:08
Last Modified: 12 Jun 2009 11:08
Published Version: http://dx.doi.org/10.1007/s00220-004-1247-8
Status: Published
Publisher: Springer Berlin / Heidelberg
Identification Number: 10.1007/s00220-004-1247-8
URI: http://eprints.whiterose.ac.uk/id/eprint/5919

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