| Title:
|
Grothendieck ring of quantum double of finite groups (English) |
| Author:
|
Dong, Jingcheng |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
3 |
| Year:
|
2010 |
| Pages:
|
869-879 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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 $2n$. (English) |
| Keyword:
|
Grothendieck ring |
| Keyword:
|
quantum double |
| Keyword:
|
Yetter-Drinfeld module |
| Keyword:
|
dihedral group |
| MSC:
|
13D15 |
| MSC:
|
16S34 |
| MSC:
|
16T05 |
| MSC:
|
19A22 |
| idZBL:
|
Zbl 1212.16057 |
| idMR:
|
MR2672420 |
| . |
| Date available:
|
2010-07-20T17:23:40Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140609 |
| . |
| Reference:
|
[1] Auslander, M., Reiten, I., Smalø, S. O.: Representation Theory of Artin Algebras.Cambridge University Press, Cambridge (1995). MR 1314422 |
| Reference:
|
[2] Drinfeld, V. G.: Quantum Groups.Proc. Int. Cong. Math. Berkeley (1986). MR 0934283 |
| Reference:
|
[3] Kassel, C.: Quantum Groups.GTM 55. Springer-Verlag (1995). Zbl 0808.17003, MR 1321145 |
| Reference:
|
[4] Majid, S.: Doubles of quasitriangular Hopf algebras.Comm. Algebra 19 (1991), 3061-3073. Zbl 0767.16014, MR 1132774, 10.1080/00927879108824306 |
| Reference:
|
[5] Montgomery, S.: Hopf Algebras and Their Actions on Rings.CBMS, Lecture in Math, Providence, RI (1993). Zbl 0793.16029, MR 1243637 |
| Reference:
|
[6] Witherspoon, S. J.: The representation ring of the quantum double of a finite group.J. Algebra 179 (1996), 305-329. Zbl 0840.19001, MR 1367852, 10.1006/jabr.1996.0014 |
| . |
