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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 $i,j,k,l\in\{1,\ldots,N\}$.

References

[RaWe15] Raum, Sven and Weber, Moritz, 2015. Easy quantum groups and quantum subgroups of a semi-direct product quantum group. Journal of Noncommutative Geometry, 9, pp.1261–1293.