$\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting

Abstract

Hopf algebroid structures on the Weyl algebra (phase space) are presented. We define the coproduct for the Weyl generators from Leibniz rule. The codomain of the coproduct is modified in order to obtain an algebra structure. We use the dual base to construct the target map and antipode. The notion of twist is analyzed for $\kappa$-deformed phase space in Hopf algebroid setting. It is outlined how the twist in the Hopf algebroid setting reproduces the full Hopf algebra structure of $\kappa$-Poincaré algebra. Several examples of realizations are worked out in details.

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Cited by in corpus (22)

• Noncommutative Spaces and Poincaré Symmetry
• Deformed Covariant Quantum Phase Spaces as Hopf Algebroids
• Kappa-Deformations: Historical Developments and Recent Results
• Remarks on simple interpolation between Jordanian twists
• Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach
• Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras
• Gauge Theory on Twisted $\kappa$-Minkowski: Old Problems and Possible Solutions
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• Twisted bialgebroids versus bialgebroids from a Drinfeld twist
• Associative realizations of $\kappa$-deformed extended Snyder model
• Quantum Twist-Deformed D=4 Phase Spaces with Spin Sector and Hopf Algebroid Structures
• Interpolations between Jordanian Twists Induced by Coboundary Twists
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Twisted conformal algebra related to $\kappa$-Minkowski space
• The Weyl realizations of Lie algebras and left-right duality
• Symmetric ordering and Weyl realizations for quantum Minkowski spaces
• $\kappa$-deformed BMS symmetry
• Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra
• One Parameter Family of Jordanian Twists
• Families of vector-like deformed relativistic quantum phase spaces, twists and symmetries
• On Light-like Deformations of the Poincaré Algebra
• Two ${\theta }_{\mu \nu }$ -deformed covariant relativistic quantum phase spaces as Poincare-Hopf algebroids