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Dynamical Yang-Baxter equation and quantum vector bundles | | J. Donin
; A. Mudrov
; | | Date: |
2 Jun 2003 | | Subject: | Quantum Algebra | math.QA | | 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, {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. | | Source: | arXiv, math.QA/0306028 | | Services: | Forum | Review | PDF | Favorites | |
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