Abstract
ABSTRACT 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 of Podleś under the assumptions and for all n=0, 1,…, three 2-dimensional covariant first order differential calculi exist if c=0, one exists if and none else. This extends a result of Podleś.
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