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Keywords:
Grothendieck ring; quantum double; Yetter-Drinfeld module; dihedral group
Grothendieck ring; quantum double; Yetter-Drinfeld module; dihedral group
Summary:
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 $2n$.
References:
[1] Auslander, M., Reiten, I., Smalø, S. O.: Representation Theory of Artin Algebras. Cambridge University Press, Cambridge (1995). MR 1314422
[2] Drinfeld, V. G.: Quantum Groups. Proc. Int. Cong. Math. Berkeley (1986). MR 0934283
[3] Kassel, C.: Quantum Groups. GTM 55. Springer-Verlag (1995). MR 1321145 | Zbl 0808.17003
[4] Majid, S.: Doubles of quasitriangular Hopf algebras. Comm. Algebra 19 (1991), 3061-3073. DOI 10.1080/00927879108824306 | MR 1132774 | Zbl 0767.16014
[5] Montgomery, S.: Hopf Algebras and Their Actions on Rings. CBMS, Lecture in Math, Providence, RI (1993). MR 1243637 | Zbl 0793.16029
[6] Witherspoon, S. J.: The representation ring of the quantum double of a finite group. J. Algebra 179 (1996), 305-329. DOI 10.1006/jabr.1996.0014 | MR 1367852 | Zbl 0840.19001
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