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We prove that a finite-dimensional Hopf algebra with the dual ChevalleyProperty over a field of characteristic zero is quasi-isomorphic to aRadford-Majid bosonization whenever the third Hochschild cohomology group inthe category of Yetter-Drinfeld modules of its diagram with coefficients in thebase field vanishes. Moreover we show that this vanishing occurs in meaningfulexamples where the diagram is a Nichols algebra.

Cohomology and Coquasi-bialgebras in the category of Yetter-Drinfeld Modules