论文标题
在Q呈现的Levi-Civita连接上
On q-deformed Levi-Civita connections
论文作者
论文摘要
我们探讨了在量子2-sphere和3-Sphere上引入Q形成的连接的可能性，以类似于Q变形的派生，满足了扭曲的Leibniz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。对于量子3-sphere上的1形模块，引入了Q形成的扭转逆转条件，我们为Levi-Civita连接的ChristOffel符号提供了明确的表达式，用于满足某些现实状况的一般指标。最后，我们在量子2-Sphere上的一类投影模块上构建度量连接。
We explore the possibility of introducing 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. For the module of 1-forms 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 satisfying a certain reality condition. Finally, we construct metric connections on a class of projective modules over the quantum 2-sphere.
