Lie algebraic deformations of Minkowski space with Poincare algebra

Abstract

We present Lie-algebraic deformations of Minkowski space with undeformed Poincaré algebra. These deformations interpolate between Snyder and $\kappa$-Minkowski space. We find realizations of noncommutative coordinates in terms of commutative coordinates and derivatives. Invariants and tensors with respect to Lorentz algebra are discussed. A general mapping from $\kappa$-deformed Snyder to Snyder space is constructed. Deformed Leibniz rule, the coproduct structure and star product are found. Special cases, particularly Snyder and $\kappa$-Minkowski in Maggiore-type realizations are discussed.

arXiv comment21 pages, no figures, Latex

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Cited by in corpus (6)

• Scalar Field Theory on Non-commutative Snyder Space-Time
• Deformed relativistic kinematics on curved spacetime -- a geometric approach
• Remarks on simple interpolation between Jordanian twists
• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
• Interpolations between Jordanian Twists Induced by Coboundary Twists
• Exponential Formulas, Normal Ordering and the Weyl-Heisenberg Algebra