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* [[Easy quantum group|Orthogonal easy quantum groups]] | * [[Easy quantum group|Orthogonal easy quantum groups]] | ||
- | * [[Free orthogonal easy quantum groups]] | + | * [[free_orthogonal_quantum_group|Free orthogonal quantum group]] ($O^+$) |
- | * [[free_orthogonal_quantum_group|Free orthogonal quantum group]] ($O^+$) | + | * [[Free symmetric quantum group]] ($S^+$) |
- | * [[Free bistochastic quantum group]] ($B^+$) | + | * //[[easy summary|...summary]]// |
- | * [[Free modified bistochastic quantum group]] ($B^{\prime +}$) | + | |
- | * [[Freely modified bistochastic quantum group]] ($B^{\# +}$) | + | |
- | * [[Free symmetric quantum group]] ($S^+$) | + | |
- | * [[Free modified symmetric quantum group]] ($S^{\prime +}$) | + | |
- | * [[Free hyperoctahedral quantum group]] ($H^+$) | + | |
- | * [[Half-liberated orthogonal easy quantum groups]] | + | |
- | * [[Half-liberated orthogonal quantum group]] ($O^\ast$) | + | |
- | * [[Half-liberated bistochastic quantum group]] ($B^{\# \ast}$) | + | |
- | * [[Half-liberated hyperoctahedral quantum group]] ($H^\ast$) | + | |
- | * [[Hyperoctahedral series]] ($H^{(\,\cdot\,)}$) | + | |
- | * [[Group-theoretical hyperoctahedral easy orthogonal quantum groups]] | + | |
- | * [[Higher hyperoctahedral series]] ($H^{[\,\cdot\,]}$) | + | |
- | * [[Non-group-theoretical hyperoctahedral easy orthogonal quantum groups]] ($H^{[\pi_{(\,\cdot\,)}]}$) | + | |
- | * [[Square commuting hyperoctahedral quantum group]] ($H^\diamond$) | + | |
- | * [[Classical orthogonal matrix groups]] | + | |
- | * [[Orthogonal group]] ($O$) | + | |
- | * [[Bistochastic group]] ($B$) | + | |
- | * [[Modified bistochastic group]] ($B'$) | + | |
- | * [[Symmetric group]] ($S$) | + | |
- | * [[Modified symmetric group]] ($S'$) | + | |
- | * [[Hyperoctahedral group]] ($H$) | + | |
* [[Unitary easy quantum group|Unitary easy quantum groups]] | * [[Unitary easy quantum group|Unitary easy quantum groups]] | ||
- | * [[Free unitary easy quantum groups]] | + | * [[Free unitary quantum group]] ($U^+$) |
- | * [[Free unitary quantum group]] ($U^+$) | + | * //[[unitary easy summary|...summary]]// |
- | * [[Half-liberated unitary quantum groups]] | + | * $q$-deformations |
- | * [[Classical unitary matrix groups]] | + | * $q$-special unitary quantum group ($SU_2^q$) |
- | * [[Unitary group]] ($U$) | + | |
- | * [[Homogeneous compact matrix quantum group|Homogeneous compact matrix quantum groups]] | + | |
- | * [[Group-theoretical quantum group|Group-theoretical quantum groups]] | + | |
- | * [[Graph-theoretical quantum group|Graph-theoretical quantum groups]] | + | |
==== Partition categories ==== | ==== Partition categories ==== | ||
- | * [[category_of_partitions|Banica–Speicher easy categories (of one-colored partitions)]] | + | * [[category_of_partitions|Banica–Speicher easy non-colored categories]] |
- | * [[Category of all partitions]] ($\mathrm{S}$) | + | * //[[easy summary|summary]]// |
- | * [[Category of partitions of even size]] ($\mathrm{S}'$) | + | * [[category_of_partitions|Colored categories]] |
- | * [[Category of all non-crossing partitions]] ($\mathrm{S}^+$) | + | * [[Categories of two-colored partitions]] |
- | * [[Category of non-crossing partitions of even size]] ($\mathrm{S}^{\prime+}$) | + | * //[[unitary easy summary|summary]]// |
- | * [[brauer category|Brauer category (of all pair partitions)]] ($\mathrm{O}$) | + | * Partitions with two-self dual colors |
- | * [[Category of pair partitions with even distances between legs]] ($\mathrm{O}^\ast$) | + | * Partitions with extra singletons |
- | * [[temperley_lieb_category|Temperley–Lieb category (of all non-crossing pair partitions)]] ($\mathrm{O}^+$) | + | * [[Linear category of partitions]] |
- | * [[Category of all partitions with small blocks]] ($\mathrm{B}$) | + | * [[Graph category]] |
- | * [[Category of partitions of even size with small blocks]] ($\mathrm{B}'$) | + | * Examples |
- | * [[Category of partitions of even size with small blocks and even distances between legs]] ($\mathrm{B}^{\#\ast}$) | + | * [[temperley_lieb_category|Temperley–Lieb category – Category of all non-crossing pairings]] |
- | * [[Category of non-crossing partitions with small blocks]] ($\mathrm{B}^+$) | + | * [[brauer category|Brauer catagory – category of all pairings]] |
- | * [[Category of non-crossing partitions of even size with small blocks]] ($\mathrm{B}^{\prime+}$) | + | * [[Category of all non-crossing partitions]] |
- | * [[Category of non-crossing partitions of even size with small blocks and even distances between legs]] ($\mathrm{B}^{\#+}$) | + | * [[Category of all partitions]] |
- | * [[Category of partitions with blocks of even size]] ($\mathrm{H}$) | + | * [[Category of all graphs]] |
- | * [[Category of partitions with blocks of even size and even distances between legs]] ($\mathrm{H}^\ast$) | + | |
- | * [[Category of non-crossing partitions with blocks of even size]] ($\mathrm{H}^+$) | + | |
- | * [[Group-theoretical hyperoctahedral categories of partitions]] | + | |
- | * [[Categories of the hyperoctahedral series]] ($\mathrm{H}^{(\,\cdot\,)}$) | + | |
- | * [[Categories of the higher hyperoctahedral series]] ($\mathrm{H}^{[\,\cdot\,]}$) | + | |
- | * [[Non-group-theoretical hyperoctahedral categories of partitions]] ($\mathrm{H}^{[\pi_{(\,\cdot\,)}]}$) | + | |
- | * [[Categories of two-colored partitions]] | + | |
- | * [[Category of all two-colored partitions]] | + | |
- | * [[Category of all non-crossing two-colored partitions]] | + | |
- | * [[Category of two-colored pair partitions]] | + | |
- | * [[Category of non-crossing two-colored pair partitions]] | + | |
- | * [[Category of two-colored pair partitions with neutral blocks]] | + | |
- | * [[Category of non-crossing two-colored pair partitions with neutral blocks]] | + | |
- | | + | |
==== Properties of CMQGs and associated algebras ==== | ==== Properties of CMQGs and associated algebras ==== | ||
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* [[Tensor product]] | * [[Tensor product]] | ||
* [[Free product]] | * [[Free product]] | ||
- | * [[Glued tensor product]] | + | * [[Glued products]] |
- | * [[Tensor Complexification]] | + | |
- | * [[Glued free product]] | + | |
- | * [[Free Complexification]] | + | |
- | * [[Self-adjoint free complexification]] | + | |
* [[Free wreath product]] | * [[Free wreath product]] | ||
* Semidirect products | * Semidirect products |