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 -