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Triangular dynamical r-matrices and quantization | | Ping Xu
; | | Date: |
1 May 2000 | | Subject: | Quantum Algebra; Symplectic Geometry | math.QA math.SG | | Abstract: | We 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. | | Source: | arXiv, math.QA/0005006 | | Services: | Forum | Review | PDF | Favorites | |
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