Explicit formulas for noncommutative deformations of ${\mathbb C}{P^N}$CPN and ${\mathbb C}{H^N}$CHN

DOI10.1063/1.4731236zbMath1276.81084arXiv1204.4030OpenAlexW3122923452MaRDI QIDQ2865538

Hiroshi Umetsu, Akifumi Sako, Toshiya Suzuki

Publication date: 29 November 2013

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

Full work available at URL: https://arxiv.org/abs/1204.4030

Mathematics Subject Classification ID

Kähler manifolds (32Q15) Geometry and quantization, symplectic methods (81S10) Deformation quantization, star products (53D55) Quantizations, deformations for selfadjoint operator algebras (46L65)

Related Items (7)

Gauge theories on noncommutative ℂPN and Bogomol’nyi-Prasad-Sommerfield-like equations ⋮ Gauge theories in noncommutative homogeneous Kähler manifolds ⋮ Deformation quantization with separation of variables for complex two-dimensional locally symmetric Kähler manifold ⋮ Fock representations and deformation quantization of Kähler manifolds ⋮ Explicit formula of deformation quantization with separation of variables for complex two-dimensional locally symmetric Kähler manifold ⋮ Noncommutative deformations of locally symmetric Kähler manifolds ⋮ Twisted Fock representations of noncommutative Kähler manifolds

Cites Work

• Existence of star-products and of formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds
• Berezin-Toeplitz quantization for compact Kähler manifolds. A review of results
• On the deformation quantization, on a Kähler manifold, associated with a Berzin quantization
• Fuzzy complex projective spaces and their star-products
• Matrix models in homogeneous spaces
• Weyl manifolds and deformation quantization
• The deformation quantizations of the hyperbolic plane
• Deformation theory and quantization. II: Physical applications
• *-products on some Kähler manifolds
• Invariant star products and representations of compact semisimple Lie groups
• Deformation quantization of Poisson manifolds
• Quantization of Kähler manifolds. IV
• Phase space reduction for star-products: An explicit construction for \(\mathbb{C} P^ n\)
• Deformation quantizations with separation of variables on a Kähler manifold
• The fuzzy sphere
• Quantization of Kahler Manifolds. II
• Poisson Geometry in Mathematics and Physics
• Generalized coherent state approach to star products and applications to the fuzzy sphere

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