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Crossed pointed categories and their equivariantizations

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 نشر من قبل Deepak Naidu
 تاريخ النشر 2011
  مجال البحث
والبحث باللغة English
 تأليف Deepak Naidu




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We propose the notion of quasi-abelian third cohomology of crossed modules, generalizing Eilenberg and MacLanes abelian cohomology and Ospels quasi-abelian cohomology, and classify crossed pointed categories in terms of it. We apply the process of equivariantization to the latter to obtain braided fusion categories which may be viewed as generalizations of the categories of modules over twisted Drinfeld doubles of finite groups. As a consequence, we obtain a description of all braided group-theoretical categories. A criterion for these categories to be modular is given. We also describe the quasi-triangular quasi-Hopf algebras underlying these categories.



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