Whitney函数的量子化
Quantization of Whitney functions
摘要：
我们研究了Whitney函数的形变量子化。为此，我们将变形量子化的概念推广到奇异集上的Whitney函数代数，并证明了辛流形闭子集上Whitney函数的变形量子化的存在性。在基本辛流形解析且奇异子集亚解析的假设下，我们确定了亚解析子集上的变形Whitney函数代数的Hochschild和循环同调与Whitney-de Rham上同调一致.最后，我们注意到如何代数指数定理惠特尼功能可以得到。
英文摘要：
We propose to study deformation quantizations of Whitney functions. To this end, we extend the notion of a deformation quantization to algebras of Whitney functions over a singular set, and show the existence of a deformation quantization of Whitney functions over a closed subset of a symplectic manifold. Under the assumption that the underlying symplectic manifold is analytic and the singular subset subanalytic, we determine that the Hochschild and cyclic homology of the deformed algebra of Whitney functions over the subanalytic subset coincide with the Whitney--de Rham cohomology. Finally, we note how an algebraic index theorem for Whitney functions can be derived.
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。
