The Brauer-Picard group of the representation category of finite supergroup algebras
Abstract
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.
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Mombelli, J. M. (2014). The Brauer-Picard group of the representation category of finite supergroup algebras. Revista de la Unión Matemática Argentina, 55 (1), 83-117. http://hdl.handle.net/11086/19337