Geodesic
Extensions of Hopf algebras
Algebra i analiz, Tome 7 (1995) no. 1, pp. 22-61 Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate the notion of exact sequences of Hopf algebras. To two Hopf algebras $A$ and $B$, and a data consisting of an action of $B$ on $A$, a cocycle, a coaction of $A$ on $B$, and a co-cocycle we associate a short exact sequence of Hopf algebras $0\to A\to C\to B\to 0$. We define cleft short exact sequences of Hopf algebras and prove that their isomorphism classes are in a bijective correspondence with the quotient set of datas as above such that the cocycle and the co-cocycle are invertible, modulo a natural action of a subgroup of $\mathrm{Reg}(B,A)$.
Keywords: Quantum Groups, Hopf Algebras. 
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     author = {N. Andruskiewitsch and J. Devoto},
     title = {Extensions of {Hopf} algebras},
     journal = {Algebra i analiz},
     pages = {22--61},
     year = {1995},
     volume = {7},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AA_1995_7_1_a1/}
}
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N. Andruskiewitsch; J. Devoto. Extensions of Hopf algebras. Algebra i analiz, Tome 7 (1995) no. 1, pp. 22-61. http://geodesic.mathdoc.fr/item/AA_1995_7_1_a1/