Geodesic
$C^*$-basic construction between non-balanced quantum doubles
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 2, pp. 611-621 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

For finite groups $X$, $G$ and the right $G$-action on $X$ by group automorphisms, the non-balanced quantum double $D(X;G)$ is defined as the crossed product $(\Bbb {C}X^{\rm op})^*\rtimes \Bbb {C}G$. We firstly prove that $D(X;G)$ is a finite-dimensional Hopf $C^*$-algebra. For any subgroup $H$ of $G$, $D(X;H)$ can be defined as a Hopf $C^*$-subalgebra of $D(X;G)$ in the natural way. Then there is a conditonal expectation from $D(X;G)$ onto $D(X;H)$ and the index is $[G;H]$. Moreover, we prove that an associated natural inclusion of non-balanced quantum doubles is the crossed product by the group algebra.
For finite groups $X$, $G$ and the right $G$-action on $X$ by group automorphisms, the non-balanced quantum double $D(X;G)$ is defined as the crossed product $(\Bbb {C}X^{\rm op})^*\rtimes \Bbb {C}G$. We firstly prove that $D(X;G)$ is a finite-dimensional Hopf $C^*$-algebra. For any subgroup $H$ of $G$, $D(X;H)$ can be defined as a Hopf $C^*$-subalgebra of $D(X;G)$ in the natural way. Then there is a conditonal expectation from $D(X;G)$ onto $D(X;H)$ and the index is $[G;H]$. Moreover, we prove that an associated natural inclusion of non-balanced quantum doubles is the crossed product by the group algebra.
DOI : 10.21136/CMJ.2024.0022-24
Classification : 16S35, 46L05
Keywords: non-balanced quantum double; $C^*$-basic construction; crossed product; action 
@article{10_21136_CMJ_2024_0022_24,
     author = {Xin, Qiaoling and Cao, Tianqing},
     title = {$C^*$-basic construction between non-balanced quantum doubles},
     journal = {Czechoslovak Mathematical Journal},
     pages = {611--621},
     year = {2024},
     volume = {74},
     number = {2},
     doi = {10.21136/CMJ.2024.0022-24},
     mrnumber = {4764543},
     zbl = {07893402},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2024.0022-24/}
}
TY  - JOUR
AU  - Xin, Qiaoling
AU  - Cao, Tianqing
TI  - $C^*$-basic construction between non-balanced quantum doubles
JO  - Czechoslovak Mathematical Journal
PY  - 2024
SP  - 611
EP  - 621
VL  - 74
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2024.0022-24/
DO  - 10.21136/CMJ.2024.0022-24
LA  - en
ID  - 10_21136_CMJ_2024_0022_24
ER  - 
%0 Journal Article
%A Xin, Qiaoling
%A Cao, Tianqing
%T $C^*$-basic construction between non-balanced quantum doubles
%J Czechoslovak Mathematical Journal
%D 2024
%P 611-621
%V 74
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2024.0022-24/
%R 10.21136/CMJ.2024.0022-24
%G en
%F 10_21136_CMJ_2024_0022_24
Xin, Qiaoling; Cao, Tianqing. $C^*$-basic construction between non-balanced quantum doubles. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 2, pp. 611-621. doi: 10.21136/CMJ.2024.0022-24

Cité par Sources :