We prove that a finite-dimensional Hopf algebra with the dual Cheval-ley 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.
Cohomology and coquasi-bialgebras in the category of Yetter-Drinfeld modules
Ardizzoni, Alessandro;Menini, Claudia
2017
Abstract
We prove that a finite-dimensional Hopf algebra with the dual Cheval-ley 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.File in questo prodotto:
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