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This article is cited in 25 scientific papers (total in 25 papers)
Research Papers
Extensions of Hopf algebras
N. Andruskiewitscha, J. Devotob a Max Planck Institute for Mathematics
b International Centre for Theoretical Physics
Abstract:
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.
Received: 24.12.1993
Citation:
N. Andruskiewitsch, J. Devoto, “Extensions of Hopf algebras”, Algebra i Analiz, 7:1 (1995), 22–61; St. Petersburg Math. J., 7:1 (1995), 17–52
Linking options:
https://www.mathnet.ru/eng/aa489 https://www.mathnet.ru/eng/aa/v7/i1/p22
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