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start [2020/02/07 07:29] amang [Compact matrix quantum groups] |
start [2021/11/23 11:56] (current) |
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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 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]] | + | |
| - | * [[Globally colorized categories]] | + | |
| - | * [[Non-crossing categories]] | + | |
| - | * [[Two-colored pair partitions]] | + | |
| ==== Properties of CMQGs and associated algebras ==== | ==== Properties of CMQGs and associated algebras ==== | ||
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| * (Co)homology of quantum groups | * (Co)homology of quantum groups | ||
| * Approximation properties ([[approximation properties summary|summary]]) | * Approximation properties ([[approximation properties summary|summary]]) | ||
| - | * Connes embedding property | + | * [[Connes embedding property]] |
| * [[Kirchberg property|Kirchberg factorization property (F)]] | * [[Kirchberg property|Kirchberg factorization property (F)]] | ||
| * [[Residual finiteness|Residual finiteness]] | * [[Residual finiteness|Residual finiteness]] | ||
| Line 89: | Line 55: | ||
| ==== Quantum group constructions ==== | ==== Quantum group constructions ==== | ||
| - | * Direct products (tensor product, free product) | + | * [[Quantum subgroup|Quantum subgroups and quotients]] |
| - | * Glued products | + | * [[Intersection of quantum groups]] |
| + | * [[Topological generation]] | ||
| + | * [[Tensor product]] | ||
| + | * [[Free product]] | ||
| + | * [[Glued products]] | ||
| + | * [[Free wreath product]] | ||
| * Semidirect products | * Semidirect products | ||
| * Wreath products | * Wreath products | ||
| - | * Topological generation | ||
| Line 101: | Line 71: | ||
| + | * Teodor Banica, //Free quantum groups and related topics// [[https://banica.u-cergy.fr/a3.pdf|Online notes]] | ||
| + | * Amaury Freslon, //Applications of non-crossing partitions to quantum groups//, lecture notes, 2019. [[https://www.imo.universite-paris-saclay.fr/~freslon/Documents/Talks/Copenhaguen_2019.pdf|Available online]] | ||
| * Sergey Neshveyev, Lars Tuset, //Compact Quantum Groups and Their Representation Categories//, Société Mathématique de France, 2013. [[https://www.sciencesmaths-paris.fr/upload/Contenu/Fichiers_chaire/livre%20Sergey%20Neyshveyev.pdf|Available online]] | * Sergey Neshveyev, Lars Tuset, //Compact Quantum Groups and Their Representation Categories//, Société Mathématique de France, 2013. [[https://www.sciencesmaths-paris.fr/upload/Contenu/Fichiers_chaire/livre%20Sergey%20Neyshveyev.pdf|Available online]] | ||
| + | * Thomas Timmermann. //An Invitation to Quantum Groups and Duality//, Zürich: European Mathematical Society (2008) | ||
| + | * Moritz Weber, //Introduction to compact (matrix) quantum groups and Banica–Speicher (easy) quantum groups//, [[https://doi.org/10.1007/s12044-017-0362-3|Proceedings – Mathematical Sciences, Vol. 127, No. 5, pp. 881–933, 2017]]. [[https://www.ias.ac.in/article/fulltext/pmsc/127/05/0881-0933|Full text online.]] | ||
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