具有量子群作用的导子
Derivations with Quantum Group Action
摘要：
霍普夫代数A的左余理想子代数B的导子与A的余乘相容（即量子齐性空间上的协变一阶微分演算，如Woronowicz所定义），它们与B的某些右理想有关。如果A作为右B-模是忠实平坦的，则对应是一一对应的。这推广了Woronowicz关于B=A的结果。给出了一阶微分学在经典点的维数的定义。对于Podles的量子2-球面S（q，c），在“q不是单位根“和“c不等于-q^（2n）/（q^（2n）+1 ^2”的条件下，对所有n= 0，1，.当c=0时，存在三个二维协变一阶微分演算，当c=-q/（q+1）^2或c=q/（-q+1）^2时，存在一个二维协变一阶微分演算，除此之外，不存在任何二维协变一阶微分演算。这扩展了Podles的结果。
英文摘要：
The derivations of a left coideal subalgebra B of a Hopf algebra A which are compatible with the comultiplication of A (that is, the covariant first order differential calculi, as defined by Woronowicz, on a quantum homogeneous space) are related to certain right ideals of B. The correspondence is one-to-one if A is faithfully flat as a right B-module. This generalizes the result for B=A due to Woronowicz. A definition for the dimension of a first order differential calculus at a classical point is given. For the quantum 2-sphere S(q,c) of Podles under the assumptions "q is not a root of unity" and "c is not equal to -q^(2n)/(q^(2n)+1)^2" for all n=0,1,..., three 2-dimensional covariant first order differential calculi exist if c=0, one exists if c=-q/(q+1)^2 or c=q/(-q+1)^2 and none else. This extends a result of Podles.
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