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Grothendieck ring of quantum double of finite groups

Jingcheng Dong (2010)

Czechoslovak Mathematical Journal

Let k G be a group algebra, and D ( k G ) its quantum double. We first prove that the structure of the Grothendieck ring of D ( k G ) can be induced from the Grothendieck ring of centralizers of representatives of conjugate classes of G . As a special case, we then give an application to the group algebra k D n , where k is a field of characteristic 2 and D n is a dihedral group of order 2 n .

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