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

• Iván Angiono ^[1] ; Alessandro Ardizzoni ^[2] ; Claudia Menini ^[3]
  1. [1] Universidad Nacional de Córdoba

     Universidad Nacional de Córdoba

     Argentina

     
  2. [2] University of Turin

     University of Turin

     Torino, Italia

     
  3. [3] University of Ferrara

     University of Ferrara

     Ferrara, Italia

     

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• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 17, Nº 2, 2017, págs. 609-653
• Idioma: inglés
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• Resumen

  • We prove that a finite-dimensional Hopf algebra with the dual Chevalley Property over a field of characteristic zero is quasi-isomorphic to a RadfordMajid 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.