Triangular dynamical r-matrices and quantization

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dc.creatorXu, Ping
dc.date2000-05-01
dc.date2001-07-31
dc.date.accessioned2026-07-07T04:34:56Z
dc.date.available2026-07-07T04:34:56Z
dc.descriptionWe provide a general study for triangular dynamical r-matrices using Poisson geometry. We show that a triangular dynamical r-matrix always gives rise to a regular Poisson manifold. Using the Fedosov method, we prove that non-degenerate (i.e., the corresponding Poisson manifolds are symplectic) triangular dynamical r-matrices (over $ \frakh^* $ and valued in $\wedge^{2}\frakg$) are quantizable, and the quantization is classified by the relative Lie algebra cohomology $H^{2}(\frakg, \frakh)[[\hbar ]]$. We also generalize this quantization method to splittable triangular dynamical r-matrices, which include all the known examples of triangular dynamical r-matrices. Finally, we arrive a conjecture that the quantization for an arbitrary triangular dynamical r-matrix is classified by the formal neighbourhood of this r-matrix in the modular space of triangular dynamical r-matrices. The dynamical r-matrix cohomology is introduced as a tool to understand such a modular space.
dc.descriptionLaTex, 43 pages, final version, typos corrected and references updated. Advances in Math, to appear
dc.identifierhttps://arxiv.org/abs/math/0005006
dc.identifierhttp://arxiv.org/abs/math/0005006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59097
dc.subjectQuantum Algebra
dc.subjectSymplectic Geometry
dc.titleTriangular dynamical r-matrices and quantization
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