Geodesic
Grothendieck ring of quantum double of finite groups
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 3, pp. 869-879

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Let $kG$ be a group algebra, and $D(kG)$ its quantum double. We first prove that the structure of the Grothendieck ring of $D(kG)$ 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 $kD_n $, where $k$ is a field of characteristic $2$ and $D_n $ is a dihedral group of order $2n$.
Let $kG$ be a group algebra, and $D(kG)$ its quantum double. We first prove that the structure of the Grothendieck ring of $D(kG)$ 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 $kD_n $, where $k$ is a field of characteristic $2$ and $D_n $ is a dihedral group of order $2n$.
Classification : 13D15, 16S34, 16T05, 19A22
Keywords: Grothendieck ring; quantum double; Yetter-Drinfeld module; dihedral group 
Dong, Jingcheng. Grothendieck ring of quantum double of finite groups. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 3, pp. 869-879. http://geodesic.mathdoc.fr/item/CMJ_2010_60_3_a17/
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     title = {Grothendieck ring of quantum double of finite groups},
     journal = {Czechoslovak Mathematical Journal},
     pages = {869--879},
     year = {2010},
     volume = {60},
     number = {3},
     mrnumber = {2672420},
     zbl = {1212.16057},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2010_60_3_a17/}
}
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