====== Free orthogonal quantum group ======

Free orthogonal quantum groups $O_N^+$ were first defined in [(:ref:Wang95)]. It is a one-parameter series of quantum groups forming a free counterpart to the orthogonal groups $O_N$


===== Definition =====

Free orthogonal quantum group of size $N$ is a compact matrix quantum group $O_N^+=(C(O_N^+),u)$, where
$$C(O_N^+)=C^*(u_{ij},\;i,j=1,\dots,n\mid u_{ij}=u_{ij}^*,\;uu^t=u^tu=1_{\mathbb{C}^N}).$$

===== Representation theory =====

===== Cohomology =====

===== Related quantum groups =====


===== References =====

[( :ref:Wang95 >>
author   : Shuzhou Wang
title    : Free products of compact quantum groups
journal  : Communications in Mathematical Physics
year     : 1995
volume   : 167
number   : 3
pages    : 671--692
url      : http://dx.doi.org/10.1007/BF02101540
)]