论文标题
编织几何形状中的cartan结构方程和李维奇连接
Cartan structure equations and Levi-Civita connection in braided geometry
论文作者
论文摘要
我们研究了代数$ a $的差分和riemannian几何形状，并具有三角形Hopf代数$ h $的作用，并且与相关编织的不兼容。一种形式的模块和编织派生的模块是$ h $ - 模块的紧凑类别中的模块，$ h $ modules $ a $ bimodules，其内部形态与张量相对应。通过将cartan演算扩展到左（右）$ a $ module连接，可以证明曲率和扭转的不同方法是等效的。 cartan结构方程和比安奇的身份得出了。证明了任意编织的对称伪式 - 里曼尼亚指标的Levi-Civita连接的存在和独特性。
We study the differential and Riemannian geometry of algebras $A$ endowed with an action of a triangular Hopf algebra $H$ and noncomutativity compatible with the associated braiding. The modules of one forms and of braided derivations are modules in a compact closed category of $H$-modules $A$-bimodules, whose internal morphisms correspond to tensor fields. Different approaches to curvature and torsion are proven to be equivalent by extending the Cartan calculus to left (right) $A$-module connections. The Cartan structure equations and the Bianchi identities are derived. Existence and uniqueness of the Levi-Civita connection for arbitrary braided symmetric pseudo-Riemannian metrics is proven.
