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- Tannaka–Krein_duality abstract "In mathematics, Tannaka–Krein duality theory concerns the interaction of a compact topological group and its category of linear representations. It is a natural extension of Pontryagin duality, between compact and discrete commutative topological groups, to groups that are compact but noncommutative. The theory is named for two men, the Soviet mathematician Mark Grigorievich Krein, and the Japanese Tadao Tannaka. In contrast to the case of commutative groups considered by Lev Pontryagin, the notion dual to a noncommutative compact group is not a group, but a category Π(G) with some additional structures, formed by the finite-dimensional representations of G. Duality theorems of Tannaka and Krein describe the converse passage from the category Π(G) back to the group G, allowing one to recover the group from its category of representations. Moreover, they in effect completely characterize all categories that can arise from a group in this fashion. Alexander Grothendieck later showed that by a similar process, Tannaka duality can be extended to the case of algebraic groups: see tannakian category. Meanwhile, the original theory of Tannaka and Krein continued to be developed and refined by mathematical physicists. A generalization of Tannaka–Krein theory provides the natural framework for studying representations of quantum groups, and is currently being extended to quantum supergroups, quantum groupoids and their dual quantum algebroids.".
- Tannaka–Krein_duality wikiPageExternalLink CT90Como.pdf.
- Tannaka–Krein_duality wikiPageExternalLink 541.
- Tannaka–Krein_duality wikiPageExternalLink 9507018+tannaka-krein+duality.
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- Tannaka–Krein_duality wikiPageRevisionID "637604520".
- Tannaka–Krein_duality wikiPageWikiLink Alexander_Grothendieck.
- Tannaka–Krein_duality wikiPageWikiLink Algebraic_group.
- Tannaka–Krein_duality wikiPageWikiLink Braided_monoidal_category.
- Tannaka–Krein_duality wikiPageWikiLink C*-category.
- Tannaka–Krein_duality wikiPageWikiLink Category:Duality_theories.
- Tannaka–Krein_duality wikiPageWikiLink Category:Harmonic_analysis.
- Tannaka–Krein_duality wikiPageWikiLink Category:Monoidal_categories.
- Tannaka–Krein_duality wikiPageWikiLink Category:Topological_groups.
- Tannaka–Krein_duality wikiPageWikiLink Category:Unitary_representation_theory.
- Tannaka–Krein_duality wikiPageWikiLink Category_(mathematics).
- Tannaka–Krein_duality wikiPageWikiLink Category_theory.
- Tannaka–Krein_duality wikiPageWikiLink Character_group.
- Tannaka–Krein_duality wikiPageWikiLink Commutative.
- Tannaka–Krein_duality wikiPageWikiLink Commutative_property.
- Tannaka–Krein_duality wikiPageWikiLink Compact_group.
- Tannaka–Krein_duality wikiPageWikiLink Contragredient_representation.
- Tannaka–Krein_duality wikiPageWikiLink Direct_sum.
- Tannaka–Krein_duality wikiPageWikiLink Drinfeld.
- Tannaka–Krein_duality wikiPageWikiLink Dual_representation.
- Tannaka–Krein_duality wikiPageWikiLink Equivariant_map.
- Tannaka–Krein_duality wikiPageWikiLink Groupoid.
- Tannaka–Krein_duality wikiPageWikiLink Groupoids.
- Tannaka–Krein_duality wikiPageWikiLink Hilbert_space.
- Tannaka–Krein_duality wikiPageWikiLink Intertwining_operator.
- Tannaka–Krein_duality wikiPageWikiLink Irreducible_representation.
- Tannaka–Krein_duality wikiPageWikiLink Lev_Pontryagin.
- Tannaka–Krein_duality wikiPageWikiLink Lie_algebroid.
- Tannaka–Krein_duality wikiPageWikiLink Linear_representation.
- Tannaka–Krein_duality wikiPageWikiLink Locally_compact.
- Tannaka–Krein_duality wikiPageWikiLink Locally_compact_space.
- Tannaka–Krein_duality wikiPageWikiLink Mark_Grigorievich_Krein.
- Tannaka–Krein_duality wikiPageWikiLink Mark_Krein.
- Tannaka–Krein_duality wikiPageWikiLink Mathematical_physics.
- Tannaka–Krein_duality wikiPageWikiLink Mathematics.
- Tannaka–Krein_duality wikiPageWikiLink Michio_Jimbo.
- Tannaka–Krein_duality wikiPageWikiLink Monoidal_category.
- Tannaka–Krein_duality wikiPageWikiLink Monoidal_unit.
- Tannaka–Krein_duality wikiPageWikiLink Natural_transformation.
- Tannaka–Krein_duality wikiPageWikiLink Noncommutative.
- Tannaka–Krein_duality wikiPageWikiLink Pontryagin_duality.
- Tannaka–Krein_duality wikiPageWikiLink Quantum_group.
- Tannaka–Krein_duality wikiPageWikiLink Quantum_groups.
- Tannaka–Krein_duality wikiPageWikiLink Rational_conformal_field_theory.
- Tannaka–Krein_duality wikiPageWikiLink Representation_theory.
- Tannaka–Krein_duality wikiPageWikiLink Subcategory.
- Tannaka–Krein_duality wikiPageWikiLink Subobject.
- Tannaka–Krein_duality wikiPageWikiLink Supergroup_(physics).
- Tannaka–Krein_duality wikiPageWikiLink Symmetric_monoidal_category.
- Tannaka–Krein_duality wikiPageWikiLink Tadao_Tannaka.
- Tannaka–Krein_duality wikiPageWikiLink Tannakian_category.
- Tannaka–Krein_duality wikiPageWikiLink Topological_group.
- Tannaka–Krein_duality wikiPageWikiLink Unitary_representation.
- Tannaka–Krein_duality wikiPageWikiLink Vladimir_Drinfeld.
- Tannaka–Krein_duality wikiPageWikiLinkText "Tannaka–Krein duality".
- Tannaka–Krein_duality wikiPageWikiLinkText "Tannaka–Krein duality#Doplicher–Roberts theorem".
- Tannaka–Krein_duality wikiPageWikiLinkText "Tannaka–Krein philosophy".
- Tannaka–Krein_duality hasPhotoCollection Tannaka–Krein_duality.
- Tannaka–Krein_duality wikiPageUsesTemplate Template:Clarify.
- Tannaka–Krein_duality subject Category:Duality_theories.
- Tannaka–Krein_duality subject Category:Harmonic_analysis.
- Tannaka–Krein_duality subject Category:Monoidal_categories.
- Tannaka–Krein_duality subject Category:Topological_groups.
- Tannaka–Krein_duality subject Category:Unitary_representation_theory.
- Tannaka–Krein_duality comment "In mathematics, Tannaka–Krein duality theory concerns the interaction of a compact topological group and its category of linear representations. It is a natural extension of Pontryagin duality, between compact and discrete commutative topological groups, to groups that are compact but noncommutative. The theory is named for two men, the Soviet mathematician Mark Grigorievich Krein, and the Japanese Tadao Tannaka.".
- Tannaka–Krein_duality label "Tannaka–Krein duality".
- Tannaka–Krein_duality sameAs m.07q15b.
- Tannaka–Krein_duality sameAs Q7683608.
- Tannaka–Krein_duality sameAs Q7683608.
- Tannaka–Krein_duality wasDerivedFrom Tannaka–Krein_duality?oldid=637604520.
- Tannaka–Krein_duality isPrimaryTopicOf Tannaka–Krein_duality.