三角动力学r-矩阵与量子化
Triangular dynamical r-matrices and quantization
摘要：
我们提供了一个一般性的研究三角动态r-矩阵使用泊松几何。我们证明了三角形动力学r-矩阵总是产生一个正则泊松流形。使用Fedosov方法，我们证明了非退化（即，相应的Poisson流形是辛的）三角动力学r-矩阵（在$ \frakh^* $上，在$\wedge^{2}\frakg$中取值）是可量化的，并且这种量化可以用相对李代数上同调$H^{2}(\frakg, \frakh)[[\hbar ]]$来分类.我们还将这种量子化方法推广到可分裂三角动态r-矩阵，其中包括所有已知的三角动态r-矩阵的例子。最后，我们得到了一个猜想，即任意三角动态r-矩阵的量子化可以通过该r-矩阵在三角动态r-矩阵的模空间中的形式邻域来分类.动力学r-矩阵上同调被引入作为理解这种模空间的工具。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
