Non-compact Hopf maps and fuzzy ultra-hyperboloids

DOI10.1016/j.nuclphysb.2012.07.017zbMath1262.81077arXiv1207.1968OpenAlexW2025066397MaRDI QIDQ1950086

Kazuki Hasebe

Publication date: 8 May 2013

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.1968

Mathematics Subject Classification ID

String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Spinor and twistor methods applied to problems in quantum theory (81R25) Noncommutative geometry in quantum theory (81R60) Smash products of general Hopf actions (16S40)

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Cites Work

• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Unnamed Item
• General concept of quantization
• N=4, d=1 supersymmetric hyper-Kähler sigma models with isospin variables
• Dimensional hierarchy in quantum Hall effects on fuzzy spheres
• Hyperboloid, instanton, oscillator
• Hopf maps, lowest Landau level, and fuzzy spheres
• Graded Hopf maps and fuzzy superspheres
• The construction of noncommutative manifolds using coherent states
• Quantum Hall effect in higher dimensions
• Unitary representations of noncompact supergroups
• Matrix configurations for spherical 4-branes and non-commutative structures on \(S^4\)
• On the Landau levels on the hyperbolic plane
• Oscillator-like unitary representations of non-compact groups with a Jordan structure and the non-compact groups of supergravity
• The fuzzy supersphere
• Chirality and Dirac operator on noncommutative sphere
• On finite 4D quantum field theory in non-commutative geometry
• On higher-dimensional fuzzy spherical branes
• Nonlinear equations for symmetric massless higher spin fields in (A)dS\(_d\)
• Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche
• Noncommutative geometry and gauge theory on fuzzy sphere
• Fuzzy spheres in AdS/CFT correspondence and holography from noncommutativity
• Noncommutative gauge theory on fuzzy four-sphere and matrix model
• Curved-space classical solutions of a massive supermatrix model
• Effective field theory description of the higher dimensional quantum Hall liquid
• Topologically nontrivial field configurations in noncommutative geometry
• Discrete series for semisimple Lie groups. II: Explicit determination of the characters
• On unitary representations of the group of de Sitter space
• A note on the representations of the De Sitter group
• Irreducible unitary representations of the Lorentz group
• Time-Reversal Symmetry in Non-Hermitian Systems
• Hyperbolic Supersymmetric Quantum Hall Effect
• On complexified mechanics and coquaternions
• Construction of Harmonic Maps Between Pseudo-Riemannian Spheres and Hyperbolic Spaces
• A natural fuzzyness of de Sitter spacetime
• Complex magnetic monopoles, geometric phases and quantum evolution in the vicinity of diabolic and exceptional points
• The fuzzy sphere
• Geometry of the three-qubit state, entanglement and division algebras
• Geometry of entangled states, Bloch spheres and Hopf fibrations
• The octonions
• Higher spin gauge theories in various dimensions
• Classification of pseudo-Riemannian submersions with totally geodesic fibres from pseudo-hyperbolic spaces
• The split algebras and noncompact Hopf maps
• Quantized Nambu–Poisson manifolds and n-Lie algebras
• On non-compact groups I. Classification of non-compact real simple Lie groups and groups containing the Lorentz group
• Discrete Series for the Universal Covering Group of the 3 + 2 de Sitter Group
• Représentations intégrables du groupe de De Sitter
• Über die Abbildungen von Sphären auf Sphäre niedrigerer Dimension
• Large \(N\) expansion from fuzzy \(\text{AdS}_2\)
• Higher-dimensional geometries from matrix brane constructions

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