Geodesic
The Grothendieck ring of quantum double of quaternion group
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 3, pp. 881-896 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Let $\Bbbk $ be an algebraically closed field of characteristic $p\neq 2$, and let $Q_8$ be the quaternion group. We describe the structures of all simple modules over the quantum double $D(\Bbbk Q_8)$ of group algebra $\Bbbk Q_8$. Moreover, we investigate the tensor product decomposition rules of all simple $D(\Bbbk Q_8)$-modules. Finally, we describe the Grothendieck ring $G_0(D(\Bbbk Q_8))$ by generators with relations.
Let $\Bbbk $ be an algebraically closed field of characteristic $p\neq 2$, and let $Q_8$ be the quaternion group. We describe the structures of all simple modules over the quantum double $D(\Bbbk Q_8)$ of group algebra $\Bbbk Q_8$. Moreover, we investigate the tensor product decomposition rules of all simple $D(\Bbbk Q_8)$-modules. Finally, we describe the Grothendieck ring $G_0(D(\Bbbk Q_8))$ by generators with relations.
DOI : 10.21136/CMJ.2024.0113-24
Classification : 16G30, 16T99
Keywords: Grothendieck ring; simple module; quantum double; quaternion group 
@article{10_21136_CMJ_2024_0113_24,
     author = {Sun, Hua and Pang, Jia and Shen, Yanxi},
     title = {The {Grothendieck} ring of quantum double of quaternion group},
     journal = {Czechoslovak Mathematical Journal},
     pages = {881--896},
     year = {2024},
     volume = {74},
     number = {3},
     doi = {10.21136/CMJ.2024.0113-24},
     mrnumber = {4804965},
     zbl = {07953683},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2024.0113-24/}
}
TY  - JOUR
AU  - Sun, Hua
AU  - Pang, Jia
AU  - Shen, Yanxi
TI  - The Grothendieck ring of quantum double of quaternion group
JO  - Czechoslovak Mathematical Journal
PY  - 2024
SP  - 881
EP  - 896
VL  - 74
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2024.0113-24/
DO  - 10.21136/CMJ.2024.0113-24
LA  - en
ID  - 10_21136_CMJ_2024_0113_24
ER  - 
%0 Journal Article
%A Sun, Hua
%A Pang, Jia
%A Shen, Yanxi
%T The Grothendieck ring of quantum double of quaternion group
%J Czechoslovak Mathematical Journal
%D 2024
%P 881-896
%V 74
%N 3
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2024.0113-24/
%R 10.21136/CMJ.2024.0113-24
%G en
%F 10_21136_CMJ_2024_0113_24
Sun, Hua; Pang, Jia; Shen, Yanxi. The Grothendieck ring of quantum double of quaternion group. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 3, pp. 881-896. doi: 10.21136/CMJ.2024.0113-24

Cité par Sources :