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Cohomology and Coquasi-bialgebras in the category of Yetter-Drinfeld Modules (1509.04844v1)
Published 16 Sep 2015 in math.QA and math.RA
Abstract: We prove that a finite-dimensional Hopf algebra with the dual Chevalley Property over a field of characteristic zero is quasi-isomorphic to a Radford-Majid bosonization whenever the third Hochschild cohomology group in the category of Yetter-Drinfeld modules of its diagram with coefficients in the base field vanishes. Moreover we show that this vanishing occurs in meaningful examples where the diagram is a Nichols algebra.