Dual κ-Minkowski spaces and κ-Poincaré algebras from Yang model and their Weyl realizations

2025/04/30 by T. Martinić-Bilać, Bilać, T. Martinić, Stjepan Meljanac +3
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Geometric Analysis and Curvature Flows #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.2504.21482

Abstract

We consider the Yang algebras isomorphic to o(1,5), o(2,4), o(3,3) and derive dual κ-Minkowski and κ-Poincaré algebras in terms of a metric g. The corresponding Weyl realization is presented and coproduct, star product and twist are computed in terms of the metric g. Finally, we construct reduced κ-Minkowski and κ-Poincaré algebras as special cases.

Citations

• Reduced Yang model and noncommutative geometry of curved spacetime
• Minimal covariant quantum space-time
• Quantum mechanics of the nonrelativistic Yang model
• Towards new relativistic doubly κ-deformed D=4 quantum phase spaces
• Fuzzy Gravity: Four-Dimensional Gravity on a Covariant Noncommutative Space and Unification with Internal Interactions
• Realizations and star-product of doubly κ-deformed Yang models
• The hidden Lorentz Covariance of Quantum Mechanics
• κ-Deformed Phase Space, Hopf Algebroid and Twisting
• Covariant Non-Commutative Space-Time
• K-Poincare-Hopf algebra and Hopf algebroid structure of phase space from twist
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• Symmetries of Snyder--de Sitter space and relativistic particle dynamics
• Differential structure on kappa-Minkowski space, and kappa-Poincare algebra
• Scalar field theory in Snyder space-time: alternatives
• Scalar Field Theory on Non-commutative Snyder Space-Time
• κ-DEFORMED SNYDER SPACETIME
• Geometry of the Grosse-Wulkenhaar Model
• Doubly special relativity in de Sitter spacetime
• Yang's Model as Triply Special Relativity and the Snyder's Model--de Sitter Special Relativity Duality
• On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
• Triply Special Relativity
• De Sitter space as an arena for doubly special relativity
• Relativistic invariant Lie algebras for kinematical observables in quantum space-time
• The quantum structure of spacetime at the Planck scale and quantum fields
• Hilbert Space Representation of the Minimal Length Uncertainty Relation
• Quantum κ-Poincare in Any Dimensions
• The algebraic structure of the generalized uncertainty principle
• A Generalized Uncertainty Principle in Quantum Gravity
• A suggestion for unifying quantum theory and relativity

Related

• Differential structure on kappa-Minkowski space, and kappa-Poincare algebra
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• Realizations and star-product of doubly κ-deformed Yang models
• The duality between κ-Poincaré algebra and κ-Poincaré group
• A note on geometry of Kappa-Minkowski space