Half-liberated easy orthogonal quantum groups are a particular class of easy orthogonal quantum groups each of which can be seen as interpolating a classical matrix group and its free, “liberated” version (without being classical or free itself). There is also a corresponding notion of half-liberated unitary easy quantum group.
An orthogonal easy quantum group associated partition category is called half-liberated if . Equivalently, the corepresentation category of contains the intertwinter for but not for .