Hopf algebra extensions of group algebras and Tambara-Yamagami categories
Abstract
Description
We determine the structure of Hopf algebra extensions 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.
Main changes appear in the description in Theorem 1.1, missing case added in proof of Proposition 6.1 and reference added. To appear in Algebr. Represent. Theory
Main changes appear in the description in Theorem 1.1, missing case added in proof of Proposition 6.1 and reference added. To appear in Algebr. Represent. Theory