TY - JOUR

T1 - Dynamical Yang-Baxter equation and quantum vector bundles

AU - Donin, J.

AU - Mudrov, A.

PY - 2005/3

Y1 - 2005/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=13844298424&partnerID=8YFLogxK

U2 - 10.1007/s00220-004-1247-8

DO - 10.1007/s00220-004-1247-8

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AN - SCOPUS:13844298424

SN - 0010-3616

VL - 254

SP - 719

EP - 760

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 3

ER -