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quantum groupoids
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(Topic)
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"quantum groupoids" is owned by bci1.
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See Also: quantum groups, groupoid C*-dynamical system, Hopf algebra, groupoid and group representations related to quantum symmetries, quantum category, quantum automata and computation, quantum space-times, locally compact groupoids, quantum fundamental groupoid, symmetry and groupoid representations in functional biology, weak Hopf C*-algebra, uniform continuity over locally compact quantum groupoids
| Other names: |
weak Hopf algebra, quantized locally compact groupoids with left Haar measure |
| Also defines: |
quantum groupoid, quantum group, extended quantum symmetries, quantum spacetime structure |
| Keywords: |
quantum groupoids, quantum groups, extended quantum symmetries, quantum spacetime structuresextended quantum symmetries, weak Hopf algebraa, quantized locally compact groupoids with left Haar measure |
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Cross-references: quantum gravity theories, foundation, points, genus, Riemann surfaces, complex structures, Lie brackets, canonical transformations, map, anchor, canonical, symplectic vector fields, Lie algebroid, Hamiltonian algebroid, algebroid structure, cotangent bundle, homogeneous space, action, lifts, infinitesimal, coordinate, transformations, quantum theories, locally compact groupoids, faithful, minimal, properties, range, subalgebra, carrier, factor, monodromy, series, matrix, generated by, gauge group, interpretation, twisted tensor product, elements, linear span, group algebra, space of functions, subgroup, discrete, Hamiltonian, Lie algebroids, conformal, quantum double, component, counit axiom, commutative diagrams, antipode map, homomorphism, counit, comultiplication, axioms, Lie groups, Lie algebras, even, quantum operator algebra, blocks, non-associative, non-commutative, noncommutative, category, object, quantum space, automorphism group, relation, invariants, quantization, higher dimensional algebra, supercategories, algebraic, fields, quantum gravity, supergravity, superfield, superalgebra, supersymmetry, structures, double groupoid, order, convolution, terms, inconsistent, type, connection, quantum field theories, coalgebras, equivalent, NOR, references, consistent, operator, algebras, Hilbert spaces, non-Abelian, source, groupoid representation, Haar measure, groupoids, locally compact, equations, groups, quantum groups, deformations, theory, symmetries, noncommutative geometry, representations, Hopf algebra, extension, left Haar measure, applications
There are 24 references to this entry.
This is version 68 of quantum groupoids, born on 2008-07-05, modified 2009-02-01.
Object id is 10751, canonical name is QuantumGroupoids2.
Accessed 2764 times total.
Classification:
| AMS MSC: | 22D25 (Topological groups, Lie groups :: Locally compact groups and their algebras :: $C^*$-algebras and $W$*-algebras in relation to group representations) | | | 55U35 (Algebraic topology :: Applied homological algebra and category theory :: Abstract and axiomatic homotopy theory) | | | 22A22 (Topological groups, Lie groups :: Topological and differentiable algebraic systems :: Topological groupoids ) | | | 55U40 (Algebraic topology :: Applied homological algebra and category theory :: Topological categories, foundations of homotopy theory) | | | 28C10 (Measure and integration :: Set functions and measures on spaces with additional structure :: Set functions and measures on topological groups, Haar measures, invariant measures) | | | 18A25 (Category theory; homological algebra :: General theory of categories and functors :: Functor categories, comma categories) | | | 18A30 (Category theory; homological algebra :: General theory of categories and functors :: Limits and colimits ) | | | 18A40 (Category theory; homological algebra :: General theory of categories and functors :: Adjoint functors ) | | | 18C10 (Category theory; homological algebra :: Categories and theories :: Theories , structure, and semantics) | | | 18D05 (Category theory; homological algebra :: Categories with structure :: Double categories, $2$-categories, bicategories and generalizations) | | | 18D20 (Category theory; homological algebra :: Categories with structure :: Enriched categories ) | | | 18D25 (Category theory; homological algebra :: Categories with structure :: Strong functors, strong adjunctions) |
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Pending Errata and Addenda
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