Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach

Abstract

We consider new Abelian twists of Poincare algebra describing non-symmetric generalization of the ones given in [1], which lead to the class of Lie-deformed quantum Minkowski spaces. We apply corresponding twist quantization in two ways: as generating quantum Poincare-Hopf algebra providing quantum Poincare symmetries, and by considering the quantization which provides Hopf algebroid describing the class of quantum relativistic phase spaces with built-in quantum Poincare covariance. If we assume that Lorentz generators are orbital i.e.do not describe spin degrees of freedom, one can embed the considered generalized phase spaces into the ones describing the quantum-deformed Heisenberg algebras.

arXiv comment15 pages,no figures; v2 with completed references, which appeared in PLB

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• Parameters of noncommutativity in Lie-algebraic noncommutative space
• Associative realizations of the extended Snyder model
• Noncommutative spaces of worldlines
• Heisenberg doubles for Snyder type models
• Generalizations of Snyder model to curved spaces
• Unification of $\kappa$-Minkowski and extended Snyder spaces
• Noncommutative Yang model and its generalizations
• Generalized Heisenberg algebra applied to realizations of the orthogonal, Lorentz and Poincare algebras and their dual extensions
• Associative realizations of $\kappa$-deformed extended Snyder model
• Quantum Twist-Deformed D=4 Phase Spaces with Spin Sector and Hopf Algebroid Structures
• Deformed Quantum Phase Spaces, Realizations, Star Products and Twists
• Generalized quantum phase spaces for the $\kappa$-deformed extended Snyder model
• Symmetries of $\kappa$ Minkowski space-time: A possibility of exotic momentum space geometry?
• Symmetric ordering and Weyl realizations for quantum Minkowski spaces
• Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra
• Two-particle system in Coulomb potential for twist-deformed space-time
• Generalized Heisenberg algebra, realizations of the $\mathfrak{gl}(n)$ algebra and applications
• Features of description of composite system's motion in twist-deformed space-time
• Two ${\theta }_{\mu \nu }$ -deformed covariant relativistic quantum phase spaces as Poincare-Hopf algebroids