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half-liberated_orthogonal_easy_quantum_groups

Half-liberated orthogonal easy quantum group

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.

Definition

An orthogonal easy quantum group $G\cong (C(G),u)$ associated partition category $\Cscr\subseteq \Pscr$ is called half-liberated if $\Cscr\cap \{\Pabab, \Pabcabc\}=\{\Pabcabc\}$. Equivalently, the corepresentation category $\FundRep(G)$ of $G$ contains the intertwinter $T_p$ for $p=\Pabcabc$ but not for $p=\Pabab$.

half-liberated_orthogonal_easy_quantum_groups.txt · Last modified: 2021/11/23 11:56 (external edit)