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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
.