Geodesic
Ore Extensions of Hopf Algebras
Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 425-434

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In this paper, Ore extensions in the class of Hopf algebras are studied. The classification theorem enables one to describe the Hopf–Ore extensions for the group algebras, for the algebras $U(\mathfrak g)$ and $U_q(\mathfrak g)$, and for the quantum "$ax+b$" group. 
@article{MZM_2003_74_3_a10,
     author = {A. N. Panov},
     title = {Ore {Extensions} of {Hopf} {Algebras}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {425--434},
     publisher = {mathdoc},
     volume = {74},
     number = {3},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2003_74_3_a10/}
}
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A. N. Panov. Ore Extensions of Hopf Algebras. Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 425-434. http://geodesic.mathdoc.fr/item/MZM_2003_74_3_a10/