论文标题
编织的交换几何形状和drinfel'd Twist变形
Braided Commutative Geometry and Drinfel'd Twist Deformations
论文作者
论文摘要
在本文中，我们给出了几类符号歧管上的Drinfel扭曲变形量化的障碍。从这种量化程序的动机中，我们进一步在任何编织的交换代数上构建了非交通性的cartan演算，以及对任何非分类均值度度量的均等的Levi-Civita协方差衍生物。这概括并统一了曲折的歧管上的cartan演算，在扭曲恒星产物代数上的cartan演算。我们证明，drinfel'd函子在编织的交换几何形状中导致等效类，并通过子曼佛代数投影通勤。
In this thesis we give obstructions for Drinfel'd twist deformation quantization on several classes of symplectic manifolds. Motivated from this quantization procedure, we further construct a noncommutative Cartan calculus on any braided commutative algebra, as well as an equivariant Levi-Civita covariant derivative for any non-degenerate equivariant metric. This generalizes and unifies the Cartan calculus on a smooth manifold and the Cartan calculus on twist star product algebras. We prove that the Drinfel'd functor leads to equivalence classes in braided commutative geometry and commutes with submanifold algebra projection.
