Free orthogonal quantum group

Free orthogonal quantum groups $O_N^+$ were first defined in [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

[Wang95] Shuzhou Wang, 1995. Free products of compact quantum groups. Communications in Mathematical Physics, 167(3), pp.671–692.

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