N维量子欧几里得空间的框架形式
Frame formalism for the N-dimensional quantum Euclidean spaces
摘要：
我们勾画了我们最近的应用程序的非交换版本的Cartan“移动框架”形式主义的量子欧几里得空间$R^N_q$，空间是协变的量子组$SO_q(N)$的作用下。对于$R^N_q$上的两个基于$R$ -矩阵形式的协变微分演算，我们分别给出了一个框架、对偶内导子、一个度量和两个曲率为零的几乎度量相容的共变导数的构造.为了获得这些结果，我们已经开发了一种技术，充分利用量子群协方差的$R^N_q$。我们首先在大代数$Ω^*(R^N_q) \cocross \uqs$中找到一个框架。然后我们定义了从$R^N_q \cocross U_q^{\pm}{so(N)}$到$R^N_q$的同态，我们使用它来将这个框架投影到$Ω^*(R^N_q)$中。
英文摘要：
We sketch our recent application of a non-commutative version of the Cartan `moving-frame' formalism to the quantum Euclidean space $R^N_q$, the space which is covariant under the action of the quantum group $SO_q(N)$. For each of the two covariant differential calculi over $R^N_q$ based on the $R$-matrix formalism, we summarize our construction of a frame, the dual inner derivations, a metric and two torsion-free almost metric compatible covariant derivatives with a vanishing curvature. To obtain these results we have developed a technique which fully exploits the quantum group covariance of $R^N_q$. We first find a frame in the larger algebra $Ω^*(R^N_q) \cocross \uqs$. Then we define homomorphisms from $R^N_q \cocross U_q^{\pm}{so(N)}$ to $R^N_q$ which we use to project this frame in $Ω^*(R^N_q)$.
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。
