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Hopf Algebra Extensions of Group Algebras and Tambara-Yamagami Categories

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Abstract

We determine the structure of Hopf algebras that admit an extension of a group algebra by the cyclic group of order 2. We study the corepresentation theory of such Hopf algebras, which provide a generalization, at the Hopf algebra level, of the so called Tambara-Yamagami fusion categories. As a byproduct, we show that every semisimple Hopf algebra of dimension < 36 is necessarily group-theoretical; thus 36 is the smallest possible dimension where a non group-theoretical example occurs.

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Authors and Affiliations

  1. Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, CIEM – CONICET, (5000) Ciudad Universitaria, Córdoba, Argentina

    Sonia Natale

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  1. Sonia Natale
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Correspondence to Sonia Natale.

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This work was partially supported by CONICET, ANPCyT, SeCYT (UNC), FaMAF and Alexander von Humboldt Foundation.

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Natale, S. Hopf Algebra Extensions of Group Algebras and Tambara-Yamagami Categories. Algebr Represent Theor 13, 673–691 (2010). https://doi.org/10.1007/s10468-009-9168-z

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