Group-theoretical quantum groups

Group-theoretical quantum groups are a particular class of compact matrix quantum groups introduced by Raum and Weber in [RaWe15].

Definition

For every $N\in \N$ any compact $N\times N$ -matrix quantum group $G\cong(C(G),u)$ is called group-theoretical if $G$ is homogeneous and the squares of the entries $\{u_{i,j}\}_{i,j=1}^N$ of the fundamental corepresentation $u$ of $G$ are central projections in $C(G)$ , i.e., if $u_{i,j}^2=(u_{i,j}^2)^\ast=(u_{i,j}^2)^2$ and $u_{i,j}^2u_{k,l}=u_{k,l}u_{i,j}^2$ for all $i,j,k,l\in\{1,\ldots,N\}$ .