====== Homogeneous compact matrix quantum group ======

** Homogeneous compact matrix quantum groups ** are a particular class of [[compact matrix quantum group|compact matrix quantum groups]] introduced by Banica, Bichon and Collins in [(:ref:BanBichColl07)].

===== Definition =====

For every $N\in\N$ any compact $N\times N$-matrix quantum group $G$ is called **homogeneous** if the [[symmetric group]] $S_N$ is a compact matrix [[compact_matrix_quantum_group#comparing_compact_matrix_quantum_groups|quantum subgroup]] of $G$, i.e., if $S_N\subseteq G$.

===== References =====

[( :ref:BanBichColl07 >>
author   : Banica Teodor and Bichon Julien and Collins Benoit
title    : The hyperoctahedral quantum group
journal  : Journal of the Ramanujan Mathematical Society
year     : 2007
volume   : 22
number   : 4
pages    : 345--384
archivePrefix: arXiv
eprint   :0701859
)]