K-Poincare-Hopf algebra and Hopf algebroid structure of phase space from twist

Abstract

We unify k-Poincare algebra and k-Minkowski spacetime by embeding them into quantum phase space. The quantum phase space has Hopf algebroid structure to which we apply the twist in order to get k- deformed Hopf algebroid structure and k-deformed phase space. We explicitly construct k-Poincare-Hopf algebra and k-Minkowski spacetime from twist. It is outlined how this construction can be extended to k-deformed super algebra including exterior derivative and forms. Our results are relevant for constructing physical theories on noncommutative spacetime by twisting Hopf algebroid phase space structure.

12 pages, minor typos corrected, published in PLA

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Cited by in corpus (29)

• Noncommutative Spaces and Poincaré Symmetry
• Twists, realizations and Hopf algebroid structure of kappa-deformed phase space
• Effects of Noncommutativity on the Black Hole Entropy
• Deformed Covariant Quantum Phase Spaces as Hopf Algebroids
• $\kappa$-Deformed Phase Space, Hopf Algebroid and Twisting
• 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
• Lie algebra type noncommutative phase spaces are Hopf algebroids
• Generalizations of Snyder model to curved spaces
• Snyder-type spaces, twisted Poincaré algebra and addition of momenta
• Universal $\kappa$-Poincaré covariant differential calculus over $\kappa$-Minkowski space
• Differential forms and k-Minkowski spacetime from extended twist
• Hermitian realizations of kappa-Minkowski spacetime
• $\kappa$-deformed phase spaces, Jordanian twists, Lorentz-Weyl algebra and dispersion relations
• Noncommutative Yang model and its generalizations
• Twisted bialgebroids versus bialgebroids from a Drinfeld twist
• Associative realizations of $\kappa$-deformed extended Snyder model
• Interpolations between Jordanian Twists Induced by Coboundary Twists
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Generalized quantum phase spaces for the $\kappa$-deformed extended Snyder model
• Symmetric ordering and Weyl realizations for quantum Minkowski spaces
• Twist for Snyder space
• On Hopf algebroid structure of kappa-deformed Heisenberg algebra
• Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra
• One Parameter Family of Jordanian Twists
• Generalized Heisenberg algebra, realizations of the $\mathfrak{gl}(n)$ algebra and applications
• Hopf algebroids with balancing subalgebra