Quantization of the Poisson SU(2) and its Poisson homogeneous space - the 2-sphere

DOI10.1007/BF02098041zbMath0719.58042MaRDI QIDQ2640212

Albert Jeu-Liang Sheu

Publication date: 1991

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Poisson structuredeformation quantization

Mathematics Subject Classification ID

Deformations of general structures on manifolds (58H15) General quantum mechanics and problems of quantization (81S99)

Related Items (44)

Quantum orbits of the \(R\)-matrix type ⋮ Noncommutative index theory for mirror quantum spheres ⋮ Leaf-preserving quantizations of Poisson SU(2) are not coalgebra homomorphisms ⋮ Twisted cyclic homology of all Podleś quantum spheres ⋮ Noncommutative balls and their doubles ⋮ Podleś spheres for the braided quantum \(\mathrm{SU}(2)\) ⋮ Poisson geometry ⋮ AdS Poisson homogeneous spaces and Drinfel’d doubles ⋮ Non-exactness of toric Poisson structures ⋮ Compact quantum group structures on type-I \(\mathrm{C}^*\)-algebras ⋮ Comparison of quantizations of symmetric spaces: cyclotomic Knizhnik–Zamolodchikov equations and Letzter–Kolb coideals ⋮ A new family of noncommutative 2-spheres ⋮ Quantized algebras of functions on homogeneous spaces with Poisson stabilizers ⋮ Strict quantization of polynomial Poisson structures ⋮ Local index formula on the equatorial Podleś sphere ⋮ The quantization of the symplectic groupoid of the standard Podlès sphere ⋮ Representations of 𝒰h (𝔰𝔲(N) ) derived from quantum flag manifolds ⋮ Spectral triples and associated Connes-de Rham complex for the quantum \(\text{SU}(2)\) and the quantum sphere ⋮ Symplectic leaves and deformation quantization ⋮ Weighted circle actions on the Heegaard quantum sphere ⋮ Nonstandard quantum complex projective line ⋮ Déformations de $C\sp*$-algèbres de Hopf ⋮ Projective Modules Over Quantum Projective Line ⋮ Covering and gluing of algebras and differential algebras ⋮ Unnamed Item ⋮ Noncommutative differential geometry on the quantum two sphere of Podlès. I: An algebraic viewpoint ⋮ Fibre product approach to index pairings for the generic Hopf fibration of SU_q(2) ⋮ Compact quantum groups and groupoid \(C^*\)-algebras ⋮ FROMC^*-ALGEBRA EXTENSIONS TO COMPACT QUANTUM METRIC SPACES, QUANTUM SU(2), PODLEŚ SPHERES AND OTHER EXAMPLES ⋮ Quantum Riemann surfaces. I: The unit disc ⋮ An obstruction to quantization of the sphere ⋮ Deformation estimates for the Berezin-Toeplitz quantization ⋮ Quantum teardrops ⋮ Some counterexamples in the theory of quantum isometry groups ⋮ Extensions and degenerations of spectral triples ⋮ Poisson-Nijenhuis structures on oriented 3D-manifolds ⋮ Vector bundles over multipullback quantum complex projective spaces ⋮ On the Haar measure of the quantum \(SU(N)\) group ⋮ Super Toeplitz operators and non-perturbative deformation quantization of supermanifolds ⋮ Quantum dressing orbits on compact groups ⋮ Representation theory of (modified) reflection equation algebra of $GL(m|n)$ type ⋮ Projections over quantum homogeneous odd-dimensional spheres ⋮ Toeplitz algebras and Rieffel deformations ⋮ The K-theory of the compact quantum group SU_q(2) for q = -1

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