Geodesic
Differential operators and differential calculus in quantum groups
Izvestiya. Mathematics , Tome 62 (1998) no. 4, pp. 673-694

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The paper deals with abstract differential operators in bialgebras and Hopf algebras (quantum groups). We prove density theorems and structure theorems for the algebras of differential operators defined by dual pairs of Hopf algebras $A$, $B$ and indicate connections with Drinfel'd's quantum double and differential geometry in quantum groups. 
@article{IM2_1998_62_4_a1,
     author = {D. P. Zhelobenko},
     title = {Differential operators and differential calculus in quantum groups},
     journal = {Izvestiya. Mathematics },
     pages = {673--694},
     publisher = {mathdoc},
     volume = {62},
     number = {4},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1998_62_4_a1/}
}
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D. P. Zhelobenko. Differential operators and differential calculus in quantum groups. Izvestiya. Mathematics , Tome 62 (1998) no. 4, pp. 673-694. http://geodesic.mathdoc.fr/item/IM2_1998_62_4_a1/