On two finiteness conditions for Hopf algebras with nonzero integral

• Nicolás Andruskiewitsch ^[1] ; Juan Cuadra ^[2] ; Pavel Etingof ^[3]
  1. [1] Universidad Nacional de Córdoba

     Universidad Nacional de Córdoba

     Argentina

     
  2. [2] Universidad de Almería

     Universidad de Almería

     Almería, España

     
  3. [3] Massachusetts Institute of Technology

     Massachusetts Institute of Technology

     City of Cambridge, Estados Unidos

     

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• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 14, Nº 2, 2015, págs. 401-440
• Idioma: inglés
• DOI: 10.2422/2036-2145.201206_011
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• Resumen

  • A Hopf algebra is co-Frobenius when it has a nonzero integral. It is proved that the composition length of the indecomposable injective comodules over a co-Frobenius Hopf algebra is bounded. As a consequence, the coradical filtration of a co-Frobenius Hopf algebra is finite; this confirms a conjecture by Sorin D˘asc˘alescu and the first author. The proof is of categorical nature and the same result is obtained for Frobenius tensor categories of subexponential growth.

    A family of co-Frobenius Hopf algebras that are not of finite type over their Hopf socles is co