Grothendieck ring of quantum double of finite groups

Jingcheng Dong

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 3, page 869-879
  • ISSN: 0011-4642

Abstract

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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 .

How to cite

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Dong, Jingcheng. "Grothendieck ring of quantum double of finite groups." Czechoslovak Mathematical Journal 60.3 (2010): 869-879. <http://eudml.org/doc/38046>.

@article{Dong2010,
abstract = {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 $2n$.},
author = {Dong, Jingcheng},
journal = {Czechoslovak Mathematical Journal},
keywords = {Grothendieck ring; quantum double; Yetter-Drinfeld module; dihedral group; Grothendieck rings; quantum doubles; Yetter-Drinfeld modules; dihedral groups},
language = {eng},
number = {3},
pages = {869-879},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Grothendieck ring of quantum double of finite groups},
url = {http://eudml.org/doc/38046},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Dong, Jingcheng
TI - Grothendieck ring of quantum double of finite groups
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 3
SP - 869
EP - 879
AB - 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 $2n$.
LA - eng
KW - Grothendieck ring; quantum double; Yetter-Drinfeld module; dihedral group; Grothendieck rings; quantum doubles; Yetter-Drinfeld modules; dihedral groups
UR - http://eudml.org/doc/38046
ER -

References

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  1. Auslander, M., Reiten, I., Smalø, S. O., Representation Theory of Artin Algebras, Cambridge University Press, Cambridge (1995). (1995) MR1314422
  2. Drinfeld, V. G., Quantum Groups, Proc. Int. Cong. Math. Berkeley (1986). (1986) MR0934283
  3. Kassel, C., Quantum Groups, GTM 55. Springer-Verlag (1995). (1995) Zbl0808.17003MR1321145
  4. Majid, S., 10.1080/00927879108824306, Comm. Algebra 19 (1991), 3061-3073. (1991) Zbl0767.16014MR1132774DOI10.1080/00927879108824306
  5. Montgomery, S., Hopf Algebras and Their Actions on Rings, CBMS, Lecture in Math, Providence, RI (1993). (1993) Zbl0793.16029MR1243637
  6. Witherspoon, S. J., 10.1006/jabr.1996.0014, J. Algebra 179 (1996), 305-329. (1996) Zbl0840.19001MR1367852DOI10.1006/jabr.1996.0014

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