Bialgebra cohomology, pointed Hopf algebras, and deformations

Details Bialgebra cohomology, pointed Hopf algebras, and deformations Bialgebra cohomology, pointed Hopf algebras, and deformations

2007-04-20

arxiv.org/abs/0704.2771v2

Mathematics

Rings and Algebras

Cohomological results in the paper were significantly improved and generalized. See new abstract for details

Scientific paper

We give explicit formulas for maps in a long exact sequence connecting bialgebra cohomology to Hochschild cohomology. We give a sufficient condition for the connecting homomorphism to be surjective. We apply these results to compute all bialgebra two-cocycles of certain Radford biproducts (bosonizations). These two-cocycles are precisely those associated to the finite dimensional pointed Hopf algebras in the recent classification of Andruskiewitsch and Schneider, in an interpretation of these Hopf algebras as graded bialgebra deformations of Radford biproducts.

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