Bialgebra cohomology, pointed Hopf algebras, and deformations |
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Authors: | Mitja Mastnak |
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Affiliation: | a Department of Mathematics and Computer Science, Saint Mary’s University, Halifax, NS B3H 3C3, Canada b Department of Mathematics, Texas A&M University, College Station, TX 77845, USA |
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Abstract: | 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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Keywords: | 16W30 16E40 |
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