Compact quantum groups and groupoid \(C^*\)-algebras

DOI10.1006/jfan.1996.2999zbMath0932.17016OpenAlexW1973807996MaRDI QIDQ676197

Albert Jeu-Liang Sheu

Publication date: 13 April 1999

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1996.2999

zbMATH Keywords

quantum groups\(C^*\)-algebrasgroupoidsquantum spaces

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) (C^*)-algebras and (W^*)-algebras in relation to group representations (22D25) Topological groupoids (including differentiable and Lie groupoids) (22A22) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89)

Related Items (9)

Quantum quaternion spheres ⋮ Quantized algebras of functions on homogeneous spaces with Poisson stabilizers ⋮ Symplectic leaves and deformation quantization ⋮ Projective Modules Over Quantum Projective Line ⋮ Operator algebra quantum homogeneous spaces of universal gauge groups ⋮ The structure of quantum spheres ⋮ Vector bundles over multipullback quantum complex projective spaces ⋮ Woronowicz construction of compact quantum groups for functions on permutations. classification result for \(N=3\) ⋮ Projections over quantum homogeneous odd-dimensional spheres

Cites Work

• The local structure of Poisson manifolds
• The structure of twisted \(SU(3)\) groups
• Algebras of functions on compact quantum groups, Schubert cells and quantum tori
• \(C^*\)-algebras of multiplication operators on Bergman spaces
• Compact matrix pseudogroups
• Quantum spheres
• Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups
• Poisson Lie groups, dressing transformations, and Bruhat decompositions
• Twisted \(\text{SU}(2)\) group. An example of a non-commutative differential calculus
• A groupoid approach to C*-algebras
• On the Haar measure of the quantum \(SU(N)\) group
• Quantum dressing orbits on compact groups
• Algebra of functions on the quantum group SU(2)
• Leaf-preserving quantizations of Poisson SU(2) are not coalgebra homomorphisms
• Quantization of the Poisson SU(2) and its Poisson homogeneous space - the 2-sphere
• C ∗ -Algebras of Multivariable Wiener-Hopf Operators
• Solutions of the classical Yang-Baxter equation for simple Lie algebras
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