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

**Free easy orthogonal quantum groups** are a particular class of [[easy_quantum_group|easy orthogonal quantum groups]] each of which can be seen as a free, "liberated", i.e., non-commutative, counterpart of a  [[classical matrix group]]. There is also a corresponding notion of [[free unitary easy quantum group]].

===== Definition =====

An [[easy_quantum_group|orthogonal easy quantum group]] $G\cong (C(G),u)$ associated partition category $\Cscr\subseteq \Pscr$ is called **free** if $\Cscr$ is //non-crossing//, i.e., if $\Cscr\subseteq \langle \fourpart, \singleton \rangle$, where the right hand side of this inclusion is the [[category of all non-crossing partitions]].