论文标题
量子球上的levi-civita连接
Levi-Civita connections on quantum spheres
论文作者
论文摘要
我们在Quantum 2-Sphere和3-Sphere上介绍了$ Q $ - 构造的连接，以类似于$ q $ defformed的派生来满足扭曲的莱布尼兹规则。我们表明，这种连接始终存在于投影模块上。此外，引入了公制兼容性的条件，并给出了明确的公式，在自由模块上参数所有度量连接。在量子3-sphere上，引入了Q形成的扭转FreeNESS条件，我们为一般指标类别的Levi-Civita连接的ChristOffel符号提供了明确的表达式。我们还对量子2-Sphere上一类射影模块进行了度量连接。最后，我们概述了具有（左）协变量和相关量子切线空间的任何HOPF代数的概括。
We introduce $q$-deformed connections on the quantum 2-sphere and 3-sphere, satisfying a twisted Leibniz rule in analogy with $q$-deformed derivations. We show that such connections always exist on projective modules. Furthermore, a condition for metric compatibility is introduced, and an explicit formula is given, parametrizing all metric connections on a free module. On the quantum 3-sphere, a q-deformed torsion freeness condition is introduced and we derive explicit expressions for the Christoffel symbols of a Levi-Civita connection for a general class of metrics. We also give metric connections on a class of projective modules over the quantum 2-sphere. Finally, we outline a generalization to any Hopf algebra with a (left) covariant calculus and associated quantum tangent space.
