B_q[SU_2]和U_q（SU_2）上的q-模糊球和量子微分
q-Fuzzy spheres and quantum differentials on B_q[SU_2] and U_q(su_2)
摘要：
经典球$C P^1$可以定义为由投影仪$e$的矩阵项与$\trace(e)=1$生成的坐标代数，模糊球以相同的方式由$\trace(e)=1+λ$定义。我们表明，标准的$q$ -球是类似的定义由$\trace_q(e)=1$和Podles 2-球的$\trace_q(e)=1+λ$，从而给出了一个统一的观点，其中2参数Podles球是$q$ -模糊球。我们进一步表明，它们出现几何“恒定时间片”的单位双曲面在$q$ -闵可夫斯基空间视为编织群$B_q[SU_2]$。然后，他们的定位同构于在$q$的固定值的$U_q(su_2)$-卡西米尔精确$q$ -变形模糊的情况下的子。利用变形和扭曲理论在一般$B_q[G]$和$U_q(g)$上引入了一个$C_q[G_C]$ -协变演算，并利用$Ω(B_q[SU_2])$给出了模糊球和Podles球上三维演算的统一观点.为了完成这幅图，我们展示了三维双交叉积时空的协变演算是如何在扭曲之前从$Ω(C_q[SU_2])$产生的。
英文摘要：
Whereas the classical sphere $C P^1$ can be defined as the coordinate algebra generated by the matrix entries of a projector $e$ with $\trace(e)=1$, the fuzzy-sphere is defined in the same way by $\trace(e)=1+λ$. We show that the standard $q$-sphere is similarly defined by $\trace_q(e)=1$ and the Podles 2-spheres by $\trace_q(e)=1+λ$, thereby giving a unified point of view in which the 2-parameter Podles spheres are $q$-fuzzy spheres. We show further that they arise geometrically as `constant time slices' of the unit hyperboloid in $q$-Minkowski space viewed as the braided group $B_q[SU_2]$. Their localisations are then isomorphic to quotients of $U_q(su_2)$ at fixed values of the $q$-Casimir precisely $q$-deforming the fuzzy case. We use transmutation and twisting theory to introduce a $C_q[G_C]$-covariant calculus on general $B_q[G]$ and $U_q(g)$, and use $Ω(B_q[SU_2])$ to provide a unified point of view on the 3D calculi on fuzzy and Podles spheres. To complete the picture we show how the covariant calculus on the 3D bicrossproduct spacetime arises from $Ω(C_q[SU_2])$ prior to twisting.
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