187 research outputs found
Structure theorems for semisimple Hopf algebras of dimension
Let be prime numbers with , and an algebraically closed
field of characteristic 0. In this paper, we obtain the structure theorems for
semisimple Hopf algebras of dimension .Comment: correct some mistakes, rewrite the section 2, and add Remark 3.
Integral modular categories of Frobenius-Perron dimension
Integral modular categories of Frobenius-Perron dimension , where
and are primes, are considered. It is already known that such categories
are group-theoretical in the cases of . In the general case we
determine that these categories are either group theoretical or contain a
Tannakian subcategory of dimension for . We then show that all
integral modular categories with
are group-theoretical, and, if in addition
, all with or are
group-theoretical. In the process we generalize an existing criterion for an
integral modular category to be group-theoretical.Comment: 15 pages, we rewrite the whole pape
Grothendieck ring of quantum double of finite groups
summary:Let be a group algebra, and its quantum double. We first prove that the structure of the Grothendieck ring of can be induced from the Grothendieck ring of centralizers of representatives of conjugate classes of . As a special case, we then give an application to the group algebra , where is a field of characteristic and is a dihedral group of order
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