The Brauer-Picard group of the representation category of finite supergroup algebras

• Martín Mombelli ^[1]
  1. [1] University of Hamburg

     University of Hamburg

     Hamburg, Freie und Hansestadt, Alemania

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 55, Nº. 1, 2014, págs. 83-117
• Idioma: inglés
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• Resumen

  • We develop further the techniques presented in a previous article (M. Mombelli. Abh. Math. Semin. Univ. Hamb. 82 (2012), 173-192), to study bimodule categories over the representation categories of arbitrary finite-dimensional Hopf algebras. We compute the Brauer-Picard group of equivalence classes of exact invertible bimodule categories over the representation categories of a certain large family of pointed non-semisimple Hopf algebras, the so called supergroup algebras (N. Andruskiewitsch, P. Etingof and S. Gelaki. Michigan Math. J. 49 (2001), 277-298). To obtain this result we first give a classification of equivalence classes of exact indecomposable bimodule categories over such Hopf algebras.